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QUESTION: 1

The discrete timefourier transform for the given signal x[n] - u[n] is

Solution:

where A is constant

The Fourier transform of odd real sequences must be purely imagenary, thus A = π

QUESTION: 2

The discrete time Fourier coefficients x[k] of the signal x [n ] =

Solution:

QUESTION: 3

The zero state respone y(k) for input f(k) = (0.8)^{k} u(k) is

Solution:

QUESTION: 4

Consider discrete time sequence

Solution:

QUESTION: 5

Consider a signal x(n) with following factors:

1. x(n) is real and even signal

2. The period of x(n) is N = 10

3. x(11) = 5

The signal x(n) is

Solution:

QUESTION: 6

Consider a discrete time signal x(n) = {-1, 2, -3, 2, -1} value of ∠x(e^{iω}) is equal to

Solution:

QUESTION: 7

A low pass filter with impulse response h_{1}(n) has spectrum H_{1} (e^{iω}) shown below.

Here only one period has been shown by reversing every second sign of h_{1}(n) a new filter having impulse response h_{2}(t) is created. The spectrum of H_{2}(e^{iω}) is given by

Solution:

QUESTION: 8

A red signal x[n] with Fourier transform x(e^{iΩ}) has following property:

1. x[n] = 0 for, n > 0

2. x [ 0] > 0

The signal x[n] is

Solution:

QUESTION: 9

A causal and stable LTI system has the property that,

The frequency response H(e^{iΩ}) for this system is

Solution:

QUESTION: 10

A 5-point sequence x[n] is given as 4 [- 3] = 1, x[ - 2] = 1, x[ -1 ] = 0 . x[0] = 5 , x[1] - 1

Let x(e^{iω}) denote the discrete time fourier transform of x[n].

The value of

Solution:

### Lecture 11: Discrete-Time Fourier Transform - Signals and Systems

Video | 55:59 min

### Lecture 10 - Discrete-Time Fourier Series - Signals and Systems

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### Discrete Time Fourier Transform

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