Noise reduction is the process of removing noise from a signal. In this project, two audio files are given: (1) speech.au and (2) noisy_speech.au. The first file contains the original speech signal and the second one contains the noisy version of the first signal. The objective of this project is to reduce the noise from the noisy file Echo and reverberation effects are used extensively in the music industry. Here we will design a digital filter that will create the echo and reverb effect on audio signals.

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Project Name: Audio Signal processing
Basic Concepts:
Audio signal processing, sometimes referred to as audio processing, is the intentional
alteration of auditory signals, or sound, often through an audio effect or effects unit. As audio
signals may be electronically represented in either digital or analog format, signal
processing may occur in either domain.
Echo to simulate the effect of reverberation in a large hall or cavern, one or several delayed
signals are added to the original signal. To be perceived as echo, the delay has to be of order
35 milliseconds or above. Short of actually playing a sound in the desired environment, the
seffect of echo can be implemented using either digital or analog methods. Analog echo
effects are implemented using tape delays and/or spring reverbs. When large numbers of
delayed signals are mixed over several seconds, the resulting sound has the effect of being
presented in a large room, and it is more commonly called reverberation or reverb for short.
When a measurement is digitized, the number of bits used to represent the measurement
determines the maximum possible signal-to-noise ratio. This is because the minimum
possible noise level is the error caused by the quantization of the signal, sometimes
called Quantization noise. This noise level is non-linear and signal-dependent; different
calculations exist for different signal models. Quantization noise is modeled as an analog
error signal summed with the signal before quantization ("additive noise").This theoretical
maximum SNR assumes a perfect input signal. If the input signal is already noisy (as is
usually the case), the signal's noise may be larger than the quantization noise. Real analog-to-
digital converters also have other sources of noise that further decrease the SNR compared to
the theoretical maximum from the idealized quantization noise, including the intentional
addition of dither.Although noise levels in a digital system can be expressed using SNR, it is
more common to use Eb/No, the energy per bit per noise power spectral density.
The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal.
Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering
that compares the level of a desiredsignal to the level of background noise. It is defined as the
ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1
(greater than 0 dB) indicates more signal than noise. While SNR is commonly quoted for
electrical signals, it can be applied to any form of signal (such as isotope levels in an ice
core or biochemical signaling between cells).The signal-to-noise ratio, the bandwidth, and
the channel capacity of a communication channel are connected by the Shannon–Hartley
theorem.Signal-to-noise ratio is sometimes used informally to refer to the ratio of
useful information to false or irrelevant data in a conversation or exchange. For example,
in online discussion forums and other online communities, off-topic posts and spam are
regarded as "noise" that interferes with the "signal" of appropriate discussion
Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful information)
and the power of background noise (unwanted signal):

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where P is average power. Both signal and noise power must be measured at the same or
equivalent points in a system, and within the same system bandwidth.
If the variance of the signal and noise are known, and the signal is zero-mean:
Objectives: 1.Reduce the noise from the noisy file.
2. Create an echo filter to make a signal converting into echo signal.
MATLAB CODES:
%Part- A
[x,Fs]=audioread('noisy_speech.au');
sound(x,Fs)
n=1:length(x);
N=length(n);
X_f=fft(x); % fft() is used to convert X in discrete Fourier Transform
(DFT) of Vector X
x_f=fftshift(X_f);% shift zero frequency component to the center of
spectrum & swaps the left and right halves of X .
magH=abs(xf);
W=((2*n)/N)-1;
subplot(2,1,1);
plot(w,magH);
title('Magnitude Response') ;
ph=angle(x_f);
subplot(2,1,2);
plot(W,ph)
title ('Phase Response');
a=1;
y=filter(b,a,x);
sound(y)
X_f=fft(y);
x_f=fftshift(X_f);
magH=abs(x_f);
figure
w=((2*n)/N)-1;
subplot(2,1,1);
plot(w,magH);
title('Magnitude Response') ;
ph=angle(x_f);
subplot(2,1,2);
plot(w,ph)
title ('Phase Response');

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Using fdatool to design a lowpass filter.
From fdatool we will export the vlue of ‘b’.
Outputs:
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
0
200
400
600
Magnitude Response
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-4
-2
0
2
4
Phase Response

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%part B
%delay = 0.375s and gain, a=0.5
[x,Fs]=audioread('speech.au');
T_d=0.375;
g=0.5;
d=round(T_d*Fs);
b=zeros(1,d+1);
a=1;
b(1)=1;
b(d+1)=g;
y=filter(b,a,x);
figure, freqz(y);
figure, impz(y(6800:7000));
sound(y,Fs)
Outputs:
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
0
200
400
600
Magnitude Response
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-4
-2
0
2
4
Phase Response
0 20 40 60 80 100 120 140 160 180 200
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
n (samples)
Amplitude
Impulse Response

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%delay = 0.375s and gain a=0.25
[x,Fs]=audioread('speech.au');
T_d=0.375;
g=0.25;
d=round(T_d*Fs);
b=zeros(1,d+1);
a=1;
b(1)=1;
b(d+1)=g;
y=filter(b,a,x);
figure, freqz(y);
figure, impz(y(6800:7000));
sound(y,Fs)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-5
0
5
x 10
4
Normalized Frequency ( rad/sample)
Phase(degrees)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-50
0
50
100
Normalized Frequency ( rad/sample)
Magnitude(dB)
0 20 40 60 80 100 120 140 160 180 200
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
n (samples)
Amplitude
Impulse Response

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%delay = 0.375s and gain a=0.75
[x,Fs]=audioread('speech.au');
T_d=0.375;
g=0.75;
d=round(T_d*Fs);
b=zeros(1,d+1);
a=1;
b(1)=1;
b(d+1)=g;
y=filter(b,a,x);
figure, freqz(y);
figure, impz(y(6800:7000));
sound(y,Fs)
Outputs:
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-5
0
5
x 10
4
Normalized Frequency ( rad/sample)
Phase(degrees)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-50
0
50
100
Normalized Frequency ( rad/sample)
Magnitude(dB)
0 20 40 60 80 100 120 140 160 180 200
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
n (samples)
Amplitude
Impulse Response

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%delay = 0.1s and 0.2s. withgain a= 0.5.
[x Fs]=audioread('speech.au');
T_d1= 0.1;
d1=round(T_d1*Fs);
g1=0.5;
T_d2= 0.2;
d2=round(T_d2*Fs);
b=zeros(1, d2+1);
b(1)=1;
b(d1+1)=g1;
b(d2+1)=g1;
a=[1];
y=filter(b, a, x);
figure, freqz(y);
figure, impz(y(6800:7000));
sound(y,Fs)
Outputs:
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-6
-4
-2
0
2
x 10
4
Normalized Frequency ( rad/sample)
Phase(degrees)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-50
0
50
100
Normalized Frequency ( rad/sample)
Magnitude(dB)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-10
-5
0
5
x 10
4
Normalized Frequency ( rad/sample)
Phase(degrees)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-50
0
50
100
Normalized Frequency ( rad/sample)
Magnitude(dB)

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Applications of this project:
Processing methods and application areas include storage, level compression, data
compression, transmission, enhancement (e.g., equalization, filtering, noise
cancellation,echo or reverb removal or addition, etc.)
Audio broadcasting
Traditionally the most important audio processing (in audio broadcasting) takes place just
before the transmitter. Studio audio processing is limited in the modern era due to digital
audio systems ( mixers, routers) being pervasive in the studio.
In audio broadcasting, the audio processor must
 prevent overmodulation, and minimize it when it occurs.
 compensate for non-linear transmitters, more common with medium
wave and shortwave broadcasting.
 adjust overall loudness to desired level.
 correct errors in audio levels .
0 20 40 60 80 100 120 140 160 180 200
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
n (samples)
Amplitude
Impulse Response