DSP Module -5 Multirate Signal Processing and its applications

By
Ms.J.Shiny Christobel, AP/ECE
Sri Ramakrishna Institute of Technology,
Coimbatore

 Multi rate DSP :
• Multi rate simply means "multiple sampling rates".
 A multi rate DSP system uses multiple sampling rates within the system.
 Whenever a signal at one rate has to be used by a system that expects a different
rate, the rate has to be increased or decreased, and some processing is required to
do so.
 Therefore "Multi rate DSP" really refers to the art or science of changing sampling
rates.
• Multi-rate processing finds use in signal processing systems where various sub-
systems with differing sample or clock rates need to be interfaced together.
 At other times multi-rate processing is used to reduce computational overhead of a
system.
 For example, an algorithm requires k operations to be completed per cycle.
 By reducing the sample rate of a signal or system by a factor of M, the arithmetic
bandwidth requirements are reduced from kfs operations to kfs/M operations per
second.
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 • The most immediate reason is when you need to pass data between two systems
which use incompatible sampling rates. For example, professional audio systems use 48
kHz rate, but consumer CD players use 44.1 kHz; when audio professionals transfer
their recorded music to CDs, they need to do a rate conversion.
 • But the most common reason is that multirate DSP can greatly increase processing
efficiency (even by orders of magnitude!), which reduces DSP system cost..
 Multirate consists of:
 • Decimation: To decrease the sampling rate,
 • Interpolation: To increase the sampling rate, or,
 • Resampling: To combine decimation and interpolation in order to change the sampling
rate by a fractional value that can be expressed as a ratio. For example, to resample by
a factor of 1.5, you just interpolate by a factor of 3 then decimate by a factor of 2 (to
change the sampling rate by a factor of 3/2=1.5.)
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1. Dual-Tone Multifrequency Signal Detection
 Dual-tone multifrequency (DTMF) signaling, increasingly being employed worldwide with push-button
telephone sets, offers a high dialing speed over the dial-pulse signaling used in conventional rotary tele-
phone sets. In recent years, DTMF signaling has also found applications requiring interactive control, such
as in voice mail, electronic mail (e-mail), telephone banking, and ATM machines
1. Spectral Analysis of Sinusoidal Signals
 An important application of digital signal processing methods is in determining in the discrete-time do- main
the frequency contents of a continuous-time signal,
more commonly known as spectral analysis. More speciﬁcally, it involves the determination of either t he
energy spectrum or the power spectrum of the signal.
1. Musical Sound Processing
 Almost all musical programs are produced in basically two stages. First, sound from each individual
instrument is recorded in an acoustically inert studio on a single track of a multitrack tape recorder.
 Then, the signals from each track are manipulated by the sound engineer to add special audio effects and
are combined in a mix-down system to ﬁnally generate the stereo recording on a two-track tape recorder.
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 Suppose we want to implement the following stable system
 The quantization error noise variance is
 Noise variance increases as |a| gets closer to the unit circle
 As |a| gets closer to 1 we have to use more bits to compensate for the
increasing error
15
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 A binary number may also have a binary point, in addition to the sign.
 The binary point is used for representing fractions, integers and integer-
fraction numbers.
 Registers are high-speed storage areas within the Central Processing Unit
(CPU) of the computer.
 All data are brought into a register before it can be processed.
 For example, if two numbers are to be added, both the numbers are brought in
registers, added, and the result is also placed in a register.
 There are two ways of representing the position of the binary point in the
register —
» Fixed point number representation
» Floating point number representation
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 The fixed point number representation assumes that the binary point is
fixed at one position either at the extreme left to make the number a
fraction, or at the extreme right to make the number an integer.
 In both cases, the binary point is not stored in the register, but the number is
treated as a fraction or integer.
 For example, if the binary point is assumed to be at extreme left, the
number 1100 is actually treated as 0.1100.
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 The integer binary signed number is represented as follows—
• For a positive integer binary number, the sign bit is 0 and the
magnitude is a positive binary number.
• For a negative integer binary number, the sign bit is 1. The magnitude is
represented in any one of the three ways—
» Signed Magnitude Representation — The magnitude is the positive
binary number itself.
» Signed 1 ’s Complement Representation — The magnitude is the 1’s
complement of the positive binary number.
» Signed 2’s Complement Representation — The magnitude is the 2’s
complement of the positive binary number.
Signed magnitude and signed 1’s complement representation are seldom used
in computer arithmetic.
09-05-2024 23

 The floating point number representation uses two registers.
 The first register stores the number without the binary point.
 The second register stores a number that indicates the position of the
binary point in the first register.
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 The floating point representation of a number has two parts
◦ —mantissa and exponent.
 The mantissa is a signed fixed point number.
 The exponent shows the position of the binary point in the mantissa.
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 Example : the binary number +11001.11 with an 8−bit mantissa and 6−bit
exponent is represented as follows—
• Mantissa is 01100111. The left most 0 indicates that the number is
positive.
• Exponent is 000101. This is the binary equivalent of decimal number + 5.
• The floating point number is Mantissa x 2exponent, i.e., + (.1100111) x 2+5
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 The arithmetic operation with the floating point numbers is complicated,
and uses complex hardware as compared to the fixed point representation.
 However, floating point calculations are required in scientific
calculations, so, computers have a built−in hardware for performing
floating point arithmetic operations.
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 Sample-rate conversion, sampling-frequency conversion or resampling is the
process of changing the sampling rate or sampling frequency of a discrete signal to
obtain a new discrete representation of the underlying continuous signal.
 Application areas include image scaling and audio/visual systems, where different
sampling rates may be used for engineering, economic, or historical reasons.
 For example, Compact Disc Digital Audio and Digital Audio Tape systems use different
sampling rates, and American television, European television, and movies all use
different frame rates.
 Sample-rate conversion prevents changes in speed and pitch that would otherwise
occur when transferring recorded material between such systems.
 More specific types of resampling
include: upsampling or upscaling; downsampling, downscaling, or decimation;
and interpolation.
 The term multi-rate digital signal processing is sometimes used to refer to systems
that incorporate sample-rate conversion.
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 Construct the zero-input limit cycle in the fixed-point
realization of
first order digital IIR filter y(n)=a y(n-1) + x(n). Assume x [0] =
7/8,
y [-1] = 0 & a = 1/2. x [n] and y [n-1] are implemented by 4-bit
registers (including Sign bit).
09-05-2024 50

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