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Compute 32 point DFT X(k) of a sinusoidal sequence of frequency 10hz without using

inbuilt functions.

Determine the first 41 samples of causal LTI system

y(n)+0.7y(n-1)-0.45y(n-2)-0.6y(n-3)-0.8y(n-4)= 0.8x(n)-0.44x(n-1)+0.36x(n-2)+0.02x(n-3)

Plot the spectra of the signal x[n]=Cos(n/3)

A signal x(t) is passed through a filter to get x1(t)

Write a program to find the symmetric and anti symmetric components of signal x[n] =

e2n

and x[n] = u[n]-u[n-10]

A signal x(t) is passed through a filter to get x1(t)

Given a system with difference equation x[n]-x[n-1] = y[n]+0.5 y[n-1] 0.5 y[n-2].

Calculate the impulse response of the system and plot the response

First order LPF described by the difference equation

y[n]-.6y(n-1)=0.2 x[n]+0.02 x[n-1]. Plot the frequency response of the system.

Filter

x1(t)x(t)

Filter

x1 tx(t)

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Determine the system function H(s) of lowest order Chebyshev and Butterworth filter

with the following specifications:

o 3dB ripple in passband 20

o 25dB attenuation in stopband 45.0

Given the following difference equation

y(n)-y(n-1)+0.9y(n-2)=x(n) for all n.Calculate and plot the impulse response h(n) at

n=-20 to 100

If x[n]={1,2,3,4},

o h1[n]={1,2,3,1}

o h2[n]={1,2,1,-1}

o Find y[n]=x[n]*h1[n]+x[n]*h2[n] and plot y[n] without using convolution

operation?

Generate a sinusoidal wave of 1khz.Calculate Nyquist frequency and verify sampling

theorem, showing the waveform for oversampled, under sampled and right sampled case.

Sample a sinusoidal waveform of 50Hz using a 1KHz sampler & plot the sampled

sequence. Vary the sampling frequency from 100Hz to 5KHz & plot the frequency

spectrum. Comment on the results.

Find the step response of the following systems:

(a)H(s)=2/(s+2)

(b)H(s)=10/(s2+7s+10)

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An LTI system has a transfer function given by

o H(z)=1+5 z-1-3 z

-2+2z

-3+5z

-8.Determine and plot the impulse response sequence

Identify the filter characterised following ideal transfer function

H(ejw) =1 ( pi/3

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Obtain the frequency response for the system function H(z) given by,

o H(z) = (1-1.618z-1+z

-2)/(1-1.516 z

-1+0.878 z

-2).

Obtain the frequency response of a low pass filter for the following specifications:

o cut-off frequency:0.5;Filter length=11

Plot the spectra of the signal x[n]=Cos(n/3)

For the given expression, y[n]= [n+2]+2 [n+1]-2 [n-1]+2 [n-2]+3 [n-3]

o

Plot a) y[-n+3]

o b) y[2n-2]

Generate a periodic triangular wave.

If x[n]={1,0.5,1}

h[n]={0.5,1}.Find the response of the system using circular convolution in frequency

domain.