P-1Classify
the following signals as one or multi-dimensional, single or multi-channel,
continuous or discrete time and analog or digital:
1.Temperature,
humidity, flow and pressure in an HVAC system.
2.HDTV
3.FM
radio
4.HD
radio
5.Internet
radio
P-2A
signal is described as f(t)=5cos(5000t) is sampled at 40000samples/sec.
1.Calculate
the sample values for one period.
2.What
is the Nyquist sampling rate for this waveform?
3.If
the samples are converted to 8 bits, find bits for each sample values.
4.What
is the quantization step value and quantization error?
5.Calculate
signal to quantization noise ratio.
P-3A
signal is given by the following equation:
x(n) = 1for n=1,2,3,4
= -2 for n=4,5,6
= 0 elsewhere.
Plot the following
signals:
1.x(n-2)
2.x(n+2)
3.x(-n)
4.x(2n)
5.x(n/2)
P-3Let
x(n)=[ XXXXXXXXXX] and y(n)=[ XXXXXXXXXX]
1.Find
cross-correlation sequence for x and y.
2.Find
autocorrelation sequence for x and y.
3.Find
the convolution sequence z(n) for x and y.
4.Plot
above three sequences using MATLAB and verify your hand calculations for those
sequences.
P-4A
system is described by the following difference equation:
y(n)=x(n)-2x(n-1)-x(n-2)-4y(n-1)-2n(y-2)
1.Find
the transfer function H(z) for this system.
2.Find
the impulse response h(n) for this system.
P-5Find
the z-transform for the following discrete-time sequences:
1.x(n)
= nsin(2n)u(n)
2.x(n)
= cos(2n)u(n)
3.x(n)
= ne -n sin(2n)u(n)
4.x(n)
= n3e-2n u(n)
5.y(n)
= x(n/2)
P-6Obtain
the inverse z-transform of the following transfer functions in all possible ROC:
1.(z3
– z)/((z-3)(z2-4z-3))
2.(z(z
– 2))/((z-1)(z-3))
3.sin(5)/(z-1
– 5)
4.7/(1
+ 0.3z-1 – 0.1z-2)
5.z/(z2
- 2z + 1)
P-7A
discrete-time system has zeros at z = 1 and z = 5 and poles at z = 2, z = 3 and
z = - 2.
1.Write
the transfer function, H(z), of this system.
2.Find
the impulse response, h(n), of this system.
3.If
a sequence x(n) = [1 1 -1] is the input to this system, determine its output
sequence, y(n).
P-8A
given sequence y(n) = [1 2 2 1] is represented by sum of polynomials in z using
Prony’s method.
1.Find
the coefficients, ci and aifor the Prony’s method.
2.Represent the series y(n), as Prony’s series
using coefficients aiand zin.
P-9For
each of the systems shown below, determine whether or not the system is linear,
time-invariant, causal and stable:
1.y(n)
= x(n+3);
2.y(n)
= x(2-n) + A, where A is a non-zero constant;
3.y(n)
= (x(n-1))2;
4.y(n)
= x(n) - y(n-1) -2y(n-2) -0.5x(n-1) – 2x(n-2).
P-10For
the initially relaxed system shown in the figure-1 below:
1.Find
the system transfer function H(z).
2.Find
the impulse response h(n) for the system.
3.Find
the inverse transfer function H-1(z).
4.Find
the impulse response h(n) for the inverse transfer functionH-1(z).
5.Is
the system described by H-1(z), causal and stable?