EX-703-C Digital Signal Processing - Nov 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aExplain the procedure of representing the sequence of samples with suitable examples. Also define the length of a discrete time signal.
   How to answer

   • Define discrete-time sequence representation (functional, tabular, graphical, sequence notation)
   • Steps to represent samples with examples
   • Definition of length of discrete-time signal
   • Example illustrating finite-length signal
2. 7 Marks
   bFind the product and addition for following two sequences $g[n] = [-21, 1.5, 3]$ for $0 \le n \le 2$ $c[n] = [3.2, 41, 36, -9.5, 0]$ for $0 \le n \le 4$ Also define Nyquist rate.
   How to answer

   • Compute element-by-element product of g[n] and c[n]
   • Compute element-by-element addition of g[n] and c[n]
   • State lengths and index ranges
   • Define Nyquist rate $f_s \ge 2f_m$
3. 7 Marks
   aDefine z-transform and region of convergence of a sequence. Also explain the causal and anti-causal systems.
   How to answer

   • Define z-transform $X(z)=\sum x[n]z^{-n}$
   • Define ROC and its significance
   • Explain causal system and its ROC
   • Explain anti-causal system and its ROC
4. 7 Marks
   bDetermine the z-transform of the finite length sequence $$x[n] = \begin{cases} \alpha^{n}; & M \le n \le N-1 \\ 0; & \text{otherwise} \end{cases}$$ Also determine its ROC.
   How to answer

   • Write z-transform summation for finite interval $M \le n \le N-1$
   • Evaluate geometric series to get $X(z)$ expression
   • Discuss ROC for finite-length sequence
   • Handle special cases for M, N and poles
5. 7 Marks
   aDiscuss the orthogonal transform pair for $x[n]$ of length N with $X[k]$ coefficients of N-point orthogonal transform.
   How to answer

   • Define N-point orthogonal basis vectors
   • Write forward transform $X[k]$ in terms of $x[n]$
   • Write inverse transform $x[n]$ in terms of $X[k]$
   • State orthogonality condition
6. 7 Marks
   bDiscuss the Discrete Fourier transform of length N-time domain sequence $x[n]$.
   How to answer

   • Define N-point DFT formula
   • Define IDFT formula
   • Explain twiddle factor $W_N$
   • Interpretation as frequency samples
7. 7 Marks
   aDescribe the direct form and cascade form of a basic FIR digital filter.
   How to answer

   • Write FIR difference equation $y[n]=\sum b_k x[n-k]$
   • Sketch direct form tapped-delay line structure
   • Explain cascade factorization into second-order sections
   • Compare complexity and modularity
8. 7 Marks
   bExplain how the total number of multipliers can be reduced. Give a suitable example.
   How to answer

   • Concept of multiplier sharing and symmetry
   • Use of linear-phase symmetry to halve multipliers
   • Example with coefficient combining
   • Quantify reduction in multiplications
9. 7 Marks
   aWrite down the applications of digital signal processing. Also differentiate the strict sense stationary and wide sense stationary processes.
   How to answer

   • List major DSP applications (speech, image, communications, biomedical)
   • Define strict-sense stationary process
   • Define wide-sense stationary process
   • Differentiate based on statistics and moments
10. 7 Marks
    bExplain the optimal filtering with suitable examples.
    How to answer

    • Define optimal filtering objective (e.g., Wiener)
    • Explain minimum mean-square error criterion
    • Describe steps with block diagram
    • Give suitable example application
11. 7 Marks
    aClassify the discrete time signal with respect to symmetry exhibited by samples with respect to time index $n = 0$, with suitable examples.
    How to answer

    • Define even/odd symmetry about n=0
    • Classify: symmetric, antisymmetric, etc.
    • Give example sequences for each class
    • Explain relevance to linear phase
12. 7 Marks
    bExplain the properties of z-transform for causal signals.
    How to answer

    • State linearity, shifting, scaling properties
    • Explain ROC for right-sided/causal signals
    • Explain initial/final value aspects
    • Relate poles to causality
13. 7 Marks
    aCompute the N-point DFT for a sequence over $0 \le n \le N-1$. $$x[n] = \begin{cases} 1; & n = 0 \\ 0; & 1 \le n \le N-1 \end{cases}$$
    How to answer

    • Apply DFT definition $X[k]=\sum_{n=0}^{N-1}x[n]W_N^{kn}$
    • Substitute $x[0]=1$, $x[n]=0$ for $n\ge 1$
    • Show $X[k]=1$ for all $k$
    • Interpret result
14. 7 Marks
    bAn IIR filter transfer function is expressed as $$H(z) = \frac{0.44z^{2} + 0.362z + 0.02}{z^{3} + 0.4z^{2} + 0.18z - 0.2}$$ Realize its direct form II with its diagram.
    How to answer

    • Rewrite $H(z)$ in terms of $z^{-1}$
    • Identify feedforward and feedback coefficients
    • Draw direct form II with shared delays
    • Label multipliers, adders and delay elements
15. 7 Marks
    aHow is stability of a system determined with z-transform?
    How to answer

    • State stability condition in z-domain
    • Explain ROC must include unit circle $|z|=1$
    • Relate poles inside unit circle for causal stable system
    • Give example check
16. 7 Marks
    bWrite short notes on any one of the following:

    1. i)Window method
    2. ii)Park-McClellan's method
    How to answer

    • Select one method (Window or Park-McClellan)
    • Explain design steps and window/equiripple concept
    • Give design equations / algorithm flow
    • Mention advantages and applications