Implementation of modified goertzel algorithm using fpga

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 10, October (2014), pp. 175-184 © IAEME
175
IMPLEMENTATION OF MODIFIED GOERTZEL
ALGORITHM USING FPGA
Ms. Benazir.H.Muntasher, Smt. Ashwini.N.Puttannavar
Electronics and Communication, AGMRCET, Varur, Hubli, India
ABSTRACT
Dual-tone Multi-frequency (DTMF) Signals are used in touch-tone telephones as well as
many other applications such as interactive control, telephone banking, and email application. There
are many DTMF decoding algorithms, but most of them cannot comply with the related International
Telecommunications Union (ITU) and Bell Communications Research, Inc. (Bell core)
recommendations and/or are not suitable for real- time implementation, but Goertzel algorithm
comply with ITU recommendations for DTMF tones detection. Earlier works implemented this
algorithm using digital signal processors. Field programmable gate arrays (FPGA) has gain
popularity in recent years due to their flexibility, parallelism and reprogram ability. The FPGA
implementation of Modified Goertzel algorithm for the DTMF tone detection is implemented in this
work. Modified Goertzel algorithm is as effective as that of normal Goertzel algorithm, and more
hardware resources are saved than that of normal Goertzel Algorithm.
In this paper, direct form-II approach is considered for designing of Modified Goertzel
algorithm for DTMF detection, mathematical model of algorithm is tested using simulink and
implemented on FPGA. This approach gives a better performance than the common filter structures
in terms of speed of operation, cost, and power consumption in real-time. The Goertzel filter is
implemented in Altera DE2-70 Cyclone-II EP2C70F896C6 FPGA kit and simulated with the help of
Quartus-II. Software WEBEDITION project navigator 9.1 was used for synthesizing and simulation
the code.
Key Terms: Modified Goertzel Algorithm, DTMF Signal Detection, MATLAB Implementation,
FPGA Implementation.
I. INTRODUCTION
In signal processing, the function of a filter is to remove unwanted parts of the signal, such as
random noise, or to extract useful parts of the signal, such as the components lying within a certain
frequency range.
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ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 10, October (2014), pp. 175-184
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A filter is an electrical network that alters the amplitude or phase characteristics of a
sinusoidal signal with respect to frequency. Ideally, a filter will not add new frequencies to the input
signal, nor will it change the component frequencies of that signal, but it will change the relative
amplitudes of the various frequency components and/or their phase relationships. Filters are often
used in electronic systems to emphasize signals in certain frequency ranges and reject signals in
other frequency ranges. There are two types of filter: analog and digital. FIR Filter is the kind of
digital filter, which can be used to perform all kinds of filtering.
1.1. FPGA: An Overview
FPGA arrived in 1984 as an alternative to programmable logic devices (PLDs) and ASICs.
FPGA offers the significant benefits of being readily programmable. An FPGA is a completely
reconfigurable computer logic chip. Like traditional hardwired gate arrays, the chip consists of a
series of logic gates. In the traditional array, these gates are specified and hard interconnected at the
manufacturing stage. The field programmable gate array differs in that it can be programmed, and re-
programmed, This has the advantages of allowing fast prototyping for applications it is intended to
be implement with hard-wired chips. FPGA can be programmed again and again, giving designers
multiple opportunities to tweak their circuits.
1.2. DTMF BACKGROUND
Table 1.1: Key pad with its Dual tone frequency
Output
770 Hz 1336 Hz Freq
Fig.1.1: DTMF tones transmitting on channel
Prior to the development of DTMF, numbers were dialed on automated telephone systems by
means of pulse dialing (Dial Pulse or DP in the U.S.) or loop disconnect (LD) signaling, which
functions by rapidly disconnecting and re-connecting the calling party telephone line, similar to
flicking a light switch on and off. The repeated interruptions of the line, as the dial spins, sounds like
a series of clicks. The exchange equipment interprets these dial pulses to determine the dialed
number. Loop disconnect range was restricted by telegraphic distortion and other technical problems,
and placing calls over longer distances required either operator assistance (operators used an earlier
kind of multi-frequency dial) or the provision of subscriber trunk dialing equipment.
Multi-frequency signaling is a group of signaling methods that use a mixture of two pure tone
sounds. Various MF signaling protocols were devised by the Bell System and CCITT. The earliest of
these were for in band signaling between switching centers, where long-distance telephone
frequency 1209
Hz
1336
Hz
1477
Hz
1633
Hz
697 Hz 1 2 3 A
770 Hz 4 5 6 B
852 Hz 7 8 9 C
941 Hz * 0 # D

177
operators used a 16-digit keypad to input the next portion of the destination telephone number in
order to contact the next downstream long-distance telephone operator. This semi-automated
signaling and switching proved successful in both speed and cost effectiveness. Based on this prior
success with using MF by specialists to establish long-distance telephone calls, Dual-tone multi-
frequency (DTMF) signaling was developed for the consumer to signal their own telephone-call's
destination telephone number instead of talking to a telephone operator.
The ITU specifications are as follows:
1. Signal frequencies:
1. Low group (Hz): 697, 770, 852, 941
2. High group (Hz): 1209, 1336, 1477, 1633
2. ITU frequency tolerances:
a. Maximum accepted frequency offset is 1.5%
b. Minimum rejected frequency offset is 3.5%
3. Signal Reception Timing:
a. Minimum accepted tone duration is 23 ms.
b. Maximum rejected tone duration is 40 ms.
c. Minimum pause time between two tones is 40 ms.
A DTMF signal consists of two superimposed sinusoidal waveforms whose frequencies are
chosen from a set of eight standardized frequencies as shown in Table 1.1. For example, by pressing
the “2” button from the Touch-tone telephone key pad, a signal made by adding a 770 Hz and a 1336
Hz sinusoid is generated as shown in figure 1.1.
1.3. Organization
Section II discusses the design stage for Goertzel filter, which includes specification of filter,
calculation of filter coefficients, and realization of filter structure.
In Section III, Results of mat lab simulation and FPGA.
In Section IV Conclusion and Future work.
SECTION II
MODIFIED GOERTZEL ALGORITHM
It is important to choose the right algorithm for detection to save memory and computation
time. The Goertzel algorithm is the optimal choice for this application because it does not use many
constants, which saves a great deal of memory space. Also, only eight DTMF frequencies need to be
calculated for this application, and the Goertzel algorithm can calculate selected frequencies. This
saves computation time. The DTMF frequency is transformed to a discrete Fourier transform (DFT)
coefficient. The relationship between the DTMF frequency (Fi) and the DFT filter coefficient (k) is
given in [9] equation (1),
k=N×
Fs
Fi
(1)
Where
Fs = Sampling frequency
N = Filter length

178
Note: k is the nearest integer to equation (1). For each k, the state variable, Vk(n), is obtained by
using the recursive difference equation shown in equation (2):
Vk(n)=x(n)+2cos(2π
N
k
)× Vk(n–1) – Vk(n–2) (2)
Where n = 0, 1,….. N
Within the same k, equation (2) is iterated until the last state variable, Vk(n), is obtained.
Thereafter, the output, Yk(n), is given in equation (3):
Yk(n)=Vk(n)+Vk(n–1) (3)
Where WN
k
= exp (–2×π×
N
k
)
This is the desired DFT value, that is, X(k) = Yk(N) for n=N, Equations (2) and (3) are
described in the direct-form realization shown in Figure(3.1). This figure gives an overview of the
entire Goertzel algorithm, so that equation (3) is computed once after equation (2) has been
calculated N+1 times. Also, k is constant when equations (2) and (3) are evaluated.
x(n) Yk(n)
Fig. 2.1: Direct form Realization of Goertzel Algorithm
The Goertzel algorithm shown in figure 2.1, is modified further based on the matched filter
concept to achieve DTMF detection. The energy of the incoming signal is calculated at the eight
DTMF frequencies. The DTMF frequency at which the incoming signal has maximum energy is the
detected frequency. This energy calculation is given in equation 4,
mag_square = |X(k)|2
(4)
max=maximum(max,mag_square) (5)
In equation 5, max is the maximum energy that initially was set to a zero value and stored in
memory. The energy from equation 4 is used for comparison with the stored maximum energy. As
soon as the new energy is greater than the stored maximum energy from the comparison, this new
energy is stored as the maximum energy for the next comparison. Also, the index that was initialized
to a zero value is changed to a number that represents the frequency of this new energy.
The comparison is performed for a total of eight times. After the final comparison, the index,
a number between 0 and 7 from the result of the comparisons, is returned to the calling program.
This number represents the detected DTMF frequency. The modified Goertzel algorithm can detect
+
Z-1
Z-1
+
Vk(n)

179
all the frequencies within an offset range of ±1.5%; however, it does not detect the frequency that
has an offset range of ±3.0%. The modified Goertzel algorithm can detect the incoming frequency
within a ±1.5% offset range.
Six tests are followed to determine if a valid DTMF digit has been detected:
1) Magnitude test: According to ITU Q.24, the maximum signal level transmit to the public network
shall not exceed −9 dBm. This limits an average voice range of −35 dBm for a very weak long-
distance call to −10 dBm for a local call. A DTMF receiver is expected to operate at an average
range of −29 to +1 dBm. Thus, the largest magnitude in each band must be greater than a
threshold of −29 dBm; otherwise, the DTMF signal should not be detected. For the magnitude
test, the squared magnitude |X(k)|2
for each DTMF frequency is computed. The largest
magnitude in each group is obtained.
2) Twist test: The tones may be attenuated according to the telephone system’s gains at the tonal
frequencies. Therefore, we do not expect the received tones to have same amplitude, even though
they may be transmitted with the same strength. Twist is defined as the difference, in decibels,
between the low and high-frequency tone levels. In practice, the DTMF digits are generated with
forward twist to compensate for greater losses at higher frequency within a long telephone cable.
For example, Australia allows 10 dB of forward twist, Japan allows only 5 dB, and North
America recommends not more than 8 dB of forward twist and 4 dB of reverse twist.
3) Frequency-offset test: This test prevents some broadband signals from being detected as DTMF
tones. If the effective DTMF tones are present, the power levels at those two frequencies should
be much higher than the power levels at the other frequencies. To perform this test, the largest
magnitude in each group is compared to the magnitudes of other frequencies in that group. The
difference must be greater than the predetermined threshold in each group.
4) Total-energy test: Similar to the frequency-offset test, the goal of total-energy test is to reject
some broadband signals to further improve the robustness of a DTMF decoder. To perform this
test, three different constants c1, c2, and c3 are used. The energy of the detected tone in the low-
frequency group is weighted by c1, the energy of the detected tone in the high-frequency group is
weighted by c2, and the sum of the two energies is weighted by c3. Each of these terms must be
greater than the summation of the energy from the rest of the filter outputs.
5) Second harmonic test: The objective of this test is to reject speech that has harmonics close to fk
so that they might be falsely detected as DTMF tones. Since DTMF tones are pure sinusoids,
they contain very little second harmonic energy. Speech, on the other hand, contains a significant
amount of second harmonic. To test the level of second harmonic, the detector must evaluate the
second harmonic frequencies of all eight DTMF tones. These second harmonic frequencies
(1394, 1540, 1704, 1882, 2418, 2672, 2954, and 3266 Hz) can also be detected using the
Goertzel algorithm. The coefficients of modified Goertzel algorithm is shown in figure 5.2.
Table 2.1: Goertzel Filter coefficients K for N=256, Fs= 8000Hz
DTMF Frequency in Hz Coefficient K=N*fi/fs
ࡲ࢏
ࡲ࢙
2cos((2*pi)/N)K
697 22.304 1.707737809
770 24.64 1.645281036
852 27.264 1.568686984
941 30.112 1.478204568
1209 38.688 1.164104023
1336 42.752 0.99637021
1477 47.264 0.798618389
1633 52.256 0.568532706

180
Fig. 2.2: Implemented architecture of Modified Goertzel Algorithm on MATLAB and FPGA
Fig 2.2 shows the block diagram which is implemented on Altera cyclone-II FPGA kit. When
the dual tone signal is applied at the Line in input of ADC which is part of CODEC from function
generator. The WM8731 CODEC present on Altera FPGA kit, will output digitized signal from
ADC which is programmed for sampling frequency of 8 kHz. The digitized signal is applied to two
FIR band pass filters. The FIR band pass filter 1 is designed with the band of 600 Hz to 1 kHz and
FIR band pass filter 2 is designed with band of 1100 Hz to 1700 Hz. The band selected for band pass
filters is on par with ITU standard shown in Table 1.1. The row frequency is in the range from 600
Hz to 1 kHz and column frequency is in the range from 1100 Hz to 2 kHz.
The output of BPF (band pass filter) is given to bank of Goertzel filters. The Goertzel filter
are designed using direct form II architecture as shown in figure 3.1, with their respective
coefficients as shown in Table 5.2 for the row and column frequencies. The Goertzel algorithm gives
high energy at the output for the frequency which it is designed and it is displayed on seven segment
display of FPGA kit. Based on the output energy and threshold set the DTMF digit detection is done.
Here the output of band pass filter is 16-bit signed integer, where as the coefficients used in Goertzel
filter are floating point as shown in Table 5.2. The Goertzel filter coefficients are represented using
IEEE 754 32-bit floating point standard. Hence the output of band pass filter which is in 16 bit
signed integer is converted to IEEE 754 32 bit floating point representation, and output is 32 bit Hex
displayed on seven segment of FPGA kit.

181
In order to establish the communication between the CODEC and FPGA the VHDL code for
SDIN and SCLK signal generation are written considering the timing constraints provided in the
User Manual as shown in figure 2.3.
Fig 2.3: Program register input timing
The I2C bus is idle when both SCLK and SDIN are at logical ‘1’. The master initiates a data
transfer by issuing a start condition, which is a high to low transition on SDIN line while SCLK line
is high as shown in figure 5.4. The bus is considered to be busy after the START condition. After
start condition, slave address is send on to the bus by master. This address is 7 bit long followed by
an eight bit R/W. Here a 0 indicates a write from the master and a ‘1’ indicates a read from the slave
to master. The master who is controlling the SCLK line will send out the bits on SDIN line, with
most significant bit send out first. The value on the SDIN line can be changed only when SCLK line
is at low.
The slave device whose address matches the address that is being sent out by the master will
respond with an acknowledgment bit on the SDA line by pulling the SDA line low during the ninth
clock cycle of the SCL line as shown in Figure 5.4. The direction bit (R/W) determines whether the
master or the slave will be the transmitter in the subsequent data transmission after the sending of the
slave address.
The one of the important feature in implementation of this project work is interfacing of
CODEC to FPGA considering timing constraint of CODEC. Here the specifications considered are
provided by assigning correct values to the registers based on the requirements. The Registers and
their contents are explained in appendix A, Table 2 and Table 3. The CODEC is used as Master and
FPGA as Slave as shown in appendix A in figure 3, means when the SCLK and SDIN signals are
given to the FPGA along with MCLK of 12.88 MHz, the CODEC in turn will give us BCLK,
ADCLRC and DACLRC so that input data can be represented.
After implementing interface part of CODEC in FPGA, VHDL codes for reading the data
from ADC is tested. The functioning of ADC and DAC is checked. The input to the ADC was an
analog signal. The frequency of the input was varied and the reconstruction provided by the DAC on
the CRO was observed.
Then, FIR Band pass filters were introduced between the ADC and DAC and the filtered
output was checked at DAC. These FIR band-pass filters coefficients were obtained from MATLAB
filter design tool (FDATOOL). The coefficients of FIR Band pass Filters designed in MATLAB are
extracted. The implementation of filter (as shown in Fig. 5.3) is further done using VHDL
programming. When band pass filters is working fine then the Goertzel filter of dual tone frequency
such as 697 Hz,770 Hz,852 Hz,941 Hz,1209 Hz,1336 Hz,1477 Hz,1633 Hz are implemented using
VHDL coding are instantiated with band pass filter in ADC and DAC program.
The output of each Goertzel filter is taken for the energy calculation. Number of samples
used in the project is 256 samples which correspond to 32 ms. Thus the output of each filter gives
256 samples which are used to find the energy, and are displayed on seven segment display of FPGA

182
kit. If input signal is 697 Hz and 1209 Hz, then the output should produce high energy for this two
tones compared to other tones, then decision is made as digit ‘1’ is pressed. Because digit ‘1’
corresponds to 697 Hz and 1209 Hz. Similarly each digit can be detected based on input dual tone
applied.
SECTION III
MATLAB AND FPGA RESULTS
Fig.3.1: Energy of 697 Hz and 1209 Hz is high correspond to digit ‘1’
Fig.3.2: Energy of 697 Hz and 1477 Hz is high corresponds to digit ‘3’
0 500 1000 1500 2000 2500 3000 3500 4000
0
200
400
600
800
Frequency (Hz)
BPFfrequencyresponses
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.5
1
1.5
Frequency (Hz)
Absoluteoutputvalues
0 500 1000 1500 2000 2500 3000 3500 4000
0
200
400
600
800
Frequency (Hz)
BPFfrequencyresponses
0 500 1000 1500 2000 2500 3000 3500 4000
0
0.5
1
Frequency (Hz)
Absoluteoutputvalues

183
SIMULINK RESULTS
Table 3.1: Energy of DTMF tones
FPGA RESULTS
Here the energy is in the form of float 32 bits hex which is displayed on seven segment
display. The output of FPGA is par with the energy that we obtain in Table 3.1.
CONCLUSION AND FUTURE SCOPE
Initially the Band Pass Filters and Goertzel filter were designed in MATLAB and the
mathematical model simulation of the design was done (as shown in fig (3.1), fig(3.2)). It has been
observed that frequency offset of the Goertzel designed filters are accepted within ±1.5% and
rejected above ±3.5%. Then the whole implementation has been done using VHDL coding. The
Analog to Digital Convertor (ADC) samples the input analog signal at 8 KHz (fs), this has been
verified by passing a sinusoidal signal as input to the ADC and increasing its frequency and
observing the DAC reconstructed signal in the CRO. It has been observed that a perfect
reconstruction is obtained until the input frequency reaches 4 KHz i.e. fs/2, after that band pass filter
and Goertzel filter are introduced after ADC. Then the functioning of the design of Goertzel filter
bank is tested by giving a dual tone signal as input to the ADC, and observed the high energy at the
output from Goertzel filter for the given dual tone signal on seven segment display on Altera
Cyclone-II FPGA kit. Hence the modified Goertzel algorithm is implemented using FPGA for
DTMF detection.
Implementation of Modified Goertzel Algorithm using FPGA can be further taken it to ASIC
design. Another future work could be proposing new frequency detection algorithm, and
implementing Goertzel algorithm using other suitable filters.
Digits frequency 697 Hz 770 Hz 852 Hz 941 Hz
1209
Hz
1336
Hz
1477
Hz
1633
Hz
1 697+1209 340100 73000 9519 2863 170000 10500 2339 890.6
2 697+1336 330000 77000 14000 2982 8552 120000 7788 1484
3 697+1477 330000 79000 11000 3247 1536 6515 120000 5638
A 697+1633 330000 81000 11000 3497 454.5 1028 4777 100000
4 770+1209 120000 360000 43000 6421 170000 10000 2430 927.3
5 770+1336 120000 360000 46000 7225 8156 120000 7956 1530
6 770+1477 120000 360000 48000 7881 1397 6306 120000 5730
B 770+1633 180000 360000 49000 8388 396.6 958.6 4653 100000
7 852+1209 29000 82000 210000 25000 170000 11000 2558 977.1
8 852+1336 27000 78000 210000 27000 7581 120000 8188 1591
9 852+1477 26000 76000 210000 29000 1224 6019 120000 5852
C 852+1633 25000 74000 210000 30000 352.3 872.4 4491 100000
* 941+1209 14000 24000 54000 250000 170000 11000 2757 1046
0 941+1336 13000 21000 51000 250000 6722 120000 8520 1674
# 941+1477 12100 20000 49000 250000 1064 5616 120000 6013
D 941+1633 11000 19000 47000 250000 414.9 774.1 4277 100000

184
REFERENCES
[1] Gay, S.L.; Hartung, J.; Smith, G.L.; , "Algorithms for multi-channel DTMF detection for the
WE DSP32 family ," Acoustics, Speech, and Signal Processing, 1989. ICASSP-89., 1989
International Conference on , vol., no., pp.1134-1137 vol.2, 23-26 May 1989
[2] Tadokoro, Y.; Haneda, Y.; , "A Dual-Tone Multifrequency Receiver Using Synchronous
Additions and Subtractions," Communications, IEEE Transactions on , vol.35, no.4,
pp. 414- 418, Apr 1987.
[3] Schwingshackl, D.; Mayerdorfer, T.; Straussnigg, D.; , "Universal Tone Detection Based on
the Goertzel Algorithm," Circuits and Systems, 2006. MWSCAS '06. 49th IEEE International
Midwest Symposium on , vol.1, no., pp.410-413, 6-9 Aug. 2006.
[4] Li-Te Shen; Shaw-Hwa Hwang; , "A new single tone detection algorithm," Communications,
Control and Signal Processing, 2008. ISCCSP 2008. 3rd International Symposium on ,
vol., no., pp.600-603, 12-14 March 2008.
[5] Kaiyi Zhang; Xiaoqing Yu; Wanggen Wan; , "A digital tone decoder based on a modified
Goertzel algorithm," Audio, Language and Image Processing, 2008. ICALIP 2008.
International Conference on , vol., no., pp.779-783, 7-9 July 2008.
[6] Li-Te Shen; Shaw-Hwa Hwang; , "A new algorithm for DTMF detection," Wireless and
Optical Communications Networks, 2009. WOCN '09. IFIP International Conference on,
vol., no., pp.1-4, 28-30 April 2009.
[7] Ekinci, Ahmet Suat; Atalar, Abdullah; , "A Fully Digital DTMF Receiver," Solid-State
Circuits Conference, 1995. ESSCIRC '95. Twenty-first European , vol., no., pp.438-441,
19-21 Sept. 1995.
[8] yongbao song; Wei Sun; Liankun Zhang; Mingming Liu; , "The software generation and the
comparison of decoding approach of DTMF signal," Control and Decision Conference
(CCDC), 2010 Chinese , vol., no., pp.1054-1057, 26-28 May 2010.
[9] Shaterian, K.; Gharaee, H.; , "DTMF detection with Goertzel algorithm using FPGA, a
resource sharing approach," Electronic Devices, Systems and Applications (ICEDSA), 2010
Intl Conf on , vol., no., pp.196-199, 11-14 April 2010.
[10] Zhang Xinyi; , "The FPGA Implementation of Modified Goertzel Algorithm for DTMF
Signal Detection," Electrical and Control Engineering (ICECE), 2010 International
Conference on , vol., no., pp.4811-4815, 25-27 June 2010.
[11] “DE2 Development and Education Board, user manual” Altera Version 1.08,
http://www.altera.com.
[12] “WM8731 Data sheet”. Wolfson Microelectronics. 2004. PDF Document.
[13] Pedroni. A. Volnei “circuit design with VHDL” 2nd
edition.
[14] Kastner. Daniel “Embedded DSP” 2002/2003.
[15] Jaya Koshta, Vineeta Saxena(Nigam) and Rakesh .K Arya, “Implementation and Validation
of Multiplier Less FPGA Based Digital Filter”, International Journal of Electronics
and Communication Engineering & Technology (IJECET), Volume 4, Issue 2, 2013,
pp. 348 - 356, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472.
[16] G.Prasad and N.Vasantha, “Design and Implementation of Multi Channel Frame
Synchronization in FPGA”, International Journal of Electronics and Communication
Engineering & Technology (IJECET), Volume 4, Issue 1, 2013, pp. 189 - 199, ISSN Print:
0976- 6464, ISSN Online: 0976 –6472.
[17] Ashish Jadhav, Prof. Minakshi Pawar, Mahesh Kumbhar, Mahesh Walunjkar and Tejas,
“Advanced Design for Implementing Dual-Tone Multi-Frequency (DTMF) as an Alternative
Mean of Communication to RF Communication”, International Journal of Electronics
and Communication Engineering & Technology (IJECET), Volume 3, Issue 2, 2012,
pp. 263 - 270, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472.

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