GATE Electrical Engineering (EE) Test: Fourier Analysis of Discrete Time

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

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

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

Consider discrete time sequence 

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

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

A low pass filter with impulse response h₁(n) has spectrum H₁ (e^iω) shown below.

Here only one period has been shown by reversing every second sign of h₁(n) a new filter having impulse response  h₂(t) is created. The spectrum of H₂(e^iω) is given by 

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

A causal and stable LTI system has the property that,

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

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