Shahjalal University of Science & Technology
Department of Electrical & Electronic Engineering
Term Test, Session: 2019-2020
Course Code: EEE331 (Digital Signal Processing-1)
Full marks: 20, Time: 30 minutes
2
1.What are thenecessary components of an ADC. Sketch the block diagram of an ADC.
6
2Show the graphical representation of the following signals, where x(n) is shown in Fig.2
() x(1) - x(n-1)
(ü) x(2n)
4
32-1 01 2 3 4
Fig.2
Þ. Express x(n) as illustrated in Fig.2 in terms of delta function.
A. Determine the z-transforms of the DT signals, z()={1,2, 5, 7,0, 1}. The up arrow(index, 0) is
at the first entry of the signal.
5. Determine the minimum sampling frequency for each of the following bandpass signals:
(i)za(t) is real with Xaf) nonzero only for 9kHz< |f|< 12kHz.
(ii)a(t) is real with Xa(f) nonzero only for 18kHz < |f|< 22kHz.
(iiüi) za(t) is complex with Xa(f) nOnzero only for 30kHz < |f| < 35kHz.
Shahjalal University of Science & Technology
Departmnent of Electrical & Electronic Engineering
grd Year 1st Semester Final Examination, 2022
Course Code: EEE 331, Session: 2019-2020
Course Title: Digital Signal Processing I
Full Marks: 100 Credit: 3.0 Exam Duration: 3 Hours
Part - A
(Answer any two of the following questions)
1 a. Write down the steps to calculate the convolution graphically. 5
10
b. Considering graphical approach, compute y(n) = z(n) *h(r). The input sequences z(n)
and the response h(n) is given in Fig.1
x(k) b(k
(a) (b)
Fig:1 4
C. Briefly explain the scaling and convolution properties.
d 6
Prove the distributive property of convolution.
8
2. Expres the sequence z<n]= {1,3, -2,4} in terms of
) Impulse sequence
(ii) Unit step sequence 7
b. Determine the z-transform of z(n) mentioned below. Also find the ROC.
C. Determine the causal signal z(n) whose z- transform is given by 5
1+2-1
X(2) = 1-z-1+0.52-2
d. Compute the auto-correlation of the signal, z(n).
z(n) = "u(n), 0<a<l
3. Find the discrete sequence, z{n] of the continuous time domain signal z.(t) which is sam
pled with sampling period T.
ze(t) = sin(2r(100t)
b Consider the analog signal 7
1
Te(t) =cos
2
(4000 t)cos(1000nt)
What is the Nyquist rate and Nyquist interval for the above signal ?
C Adigital communication link carries binary-coded words representing samples of an input
signal.
ze(t) = 3cos(6007t)+2cos(18007t)
The link is operated at 10000 bits/s and each input sample is quantizedi into 1024 difer
ent voltage levels.
(i) What are the sampling frequency and the folding frequency in Hz?
(i1) What is the Nyquist rate for the signal z.(t) in Hz?
(iü) What is the resolution of quantization A? 5
d. What is aliasing? What can be done to reduce aliasing?
Part - B
(Answer any two of following questions)
4.
Given the sequence z(n) = (6 - n)lu(n) - u(n -6)], make a sketch of
() y1(n) = a(4- n) (i) ya(n) = z(2n - 3)
(ii) ys(n) = r8-3n) (iv) ya(n) = z(n?- 2rn + 1)
b With a given sequence 5
Compute the power in z(n).
C A linear shift-invariant system has a unit sample response 6
h(n) = u-n-1)
For the input z(n) = -n3 u(n), find the output of the system.
Determine whether or not the signals below are periodic and, for each signal that is peri 6
odic, determine the fundamental period
(i) z(n) = cos(0.125Tn)
(ii) z(n) = sin( +0.2n)
(ii) z(n) = ei"cos(na/17)
5. a. Determine the Fourier transform of the signal. 6
z(n) = 0.A, -M Sn<M
elsewhere
Also find |X (w) and ZX (w).
b Write down the properties of discrete Fourier transform. What are
the drawbacks while 6
computing DFT directly?
C. Find the solution to the diference equation
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y(n) -0.25y(n - 2) = z(n)
For t(n) = u(n) and
assuming initial conditions of y(-1) =1 and yl-2) = 0.
The first five points of the
i0.3018, 0, 0.125- j0.0518,eight-point
of DFT of a real-valued
0]. Determine the remaining sequence are [0.25, 0.125 - 6
points.
6 a. Use the window design method to design a linear phase FIR filter of
order N = 24 to 8
approximnate the following ideal frequency response magnitude:
|Halele) = 0,
ol s 0.2r
0.27< wl<n
b What do you understand by FIR and IIR system?
C. Find the Kaiser window parameters, B andN, to
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frequency we = T/2, a stop-band ripple o, = 0.002,design
a low-pass filter with a cutoff 5
than 0.1m. and a transition bandwidth no greater
d Design a low-pass Butterworth filter that has a 3dB
attenuation of 40dB at 3.OkHz. cutoff frequency of 1.5kHz and an 5
e. Write down few properties of delta function.
