solution

Write a program that creates a 1 3 2048 vector x of white noise uniformly distributed over f2.=, .=g. The program should then compute and display the following.

 (a) The average power Px, the predicted average power Pv, and the percent error in Px. (b) Plot the estimated power density spectrum using Bartlett’s method with L = =12. Use a y-axis range of f0, 1g. In the plot title, print L and the estimated variance 2 B of the power density spectrum. (c) Repeat part (b), but use L = 32.

Q1=0:

Let x(k) be an N-point white noise signal uniformly distributed over f21, 1g where N = 4096. Write a program that performs the following tasks.

(a) Create x(k) and then compute and plot the normalized circular autocorrelation, xx(k). (b) Compute cxx(k) and use the result to compute and plot the power density spectrum of x(k). (c) Compute and print the average power Px.

Q1=1:

Consider the following digital filter of order m = 2p where p = 20.

(a) Compute and plot the impulse response h(k) for 0 # k , N where N = 64. (b) Compute and plot the magnitude response A( f ) for 0 # f # fsy2. (c) What type of filter is this, FIR or IIR? What range of frequencies gets passed by this filter?

Q1=2:

Consider the following digital filter of order n where n = 11 and r = .98.

Suppose fs = 2200 Hz. Write a program that uses filter to do the following. (a) Compute and plot the impulse response h(k) for 0 # k , N where N = 1001. (b) Compute and plot the magnitude response A( f ) for 0 # f # fsy2. (c) What type of filter is this, FIR or IIR? Which frequencies get rejected by this filter?

Q1=3:

Consider the following first order IIR filter.

(a) Compute and sketch the magnitude response A( f ). (b) What type of filter is this (lowpass, highpass, bandpass, bandstop)? (c) Suppose Fp = .4fs. Find the passband ripple p. (d) Suppose Fs = .2fs. Find the stopband attenuation .

Q1=4:

A bandpass filter has a sampling frequency of fs = 2000 Hz and satisfies the following design specifications.

fFs1, Fp1, Fp2, Fs2, p,  }= f200, 300, 600, 700, .1=, .0=g

(a) Find the logarithmic passband ripple, Ap. (b) Find the logarithmic stopband attenuation, As. (c) Using a logarithmic scale, sketch the shaded passband and stopband regions that A( f ) must lie within.

Q1==:

A bandstop filter has a sampling frequency of fs = 200 Hz and satisfies the following design specifications.

(a) Find the linear passband ripple, p. (b) Find the linear stopband attenuation, s. (c) Using a linear scale, sketch the shaded passband and stopband regions that A( f ) must lie within.

 Q1=6:

Consider the following FIR filter of order M 2 1 known as a running average filter

(a) Find the impulse response of this filter. (b) Is

 this a linear-phase filter? If so, what type? (c) Find the group delay of this filter.

A linear-phase FIR filter H(z) of order m = 8 has zeros at z = 6j.= and z = 6.8.

(a) Find the remaining zeros of H(z) and sketch the poles and zeros in the complex plane. (b) The DC gain of the filter is 2. Find the filter transfer function H(z). (c) Suppose the input signal gets delayed by 20 ms as it passes through this filter. What is the sampling frequency, fs?

Q1=7:

Consider a type 1 FIR linear-phase filter of order m = 2 with coefficient vector b = f1, 1, 1g T.

(a) Find the transfer function, H(z). (b) Find the amplitude response, Ar( f ). (c) Find the zeros of H(z).

Consider a type 2 FIR linear-phase filter of order m = 1 with coefficient vector b = f1, 1g T.

(a) Find the transfer function, H(z). (b) Find the amplitude response, Ar( f ). (c) Find the zeros of H(z).

Q1=8:

Consider a type 3 FIR linear-phase filter of order m = 2 with coefficient vector b = f1, 0, 21g T.

(a) Find the transfer function, H(z). (b) Find the amplitude response, Ar( f ). (c) Find the zeros of H(z).

Consider a type 4 FIR linear-phase filter of order m = 1 with coefficient vector b = f1, 21g T.

(a) Find the transfer function, H(z). (b) Find the amplitude response, Ar( f ). (c) Find the zeros of H(z).

Q1=9:

Consider the following FIR filter.

(a) Is this a linear-phase filter? If so, what is the type? (b) Sketch a signal flow graph showing a direct-form II realization of H(z) as in Section =.1. (c) Using the MATLAB function roots find the zeros of H(z). Then sketch a signal flow graph showing a cascade form realization of H(z).