Practice Problems for Digital Signal Processing (e.g., ECE438)

Collectively solved practice problems related to Digital Signal Processing

• Basic material and review
  • What is the norm of a complex exponential?

• Summation exercises
  • Compute this sum
  • Compute this other sum
  • ... and this other sum
  • When is this summation formula valid?

• CTFT exercises
  • Obtain the Fourier transform in terms of f of a step function (from FT in terms of omega)
  • Compute the Fourier transform of a rect and a sinc
  • What is the Fourier transform of a complex exponential?

• DTFT exercise
  • What is the Fourier transform of this DT cosine?
  • What is the Fourier transform of this DT rect function?

• Sampling and Nyquist Rate
  • Playing an A 440 with MATLAB
  • What kind of signals are band limited?
  • Practice Question on frequency domain view of sampling)

• Z-transform and inverse z-transform
  • Prove the scaling property of the z-transform
  • compute the z-transform of this function
  • Practice Question on z-transform computation
  • Practice Question on inverse z-transform computation)

• DFT
  • Compute this DFT
  • Compute this other DFT
  • What is the effect of zero padding on the DFT?
  • Practice question on DFT computation)

• Spectral Analysis of continuous-space (2D) signals
  • Obtain the continuous-space Fourier transform of a complex exponential
  • Obtain the continuous-space Fourier transform of a 2D rect
  • Obtain the continuous-space Fourier transform of a 2D sinc

• Spectral Analysis of discrete-space (2D) signals
  • Obtain the discrete-space Fourier transform of a rectangle
  • Compute the discrete-space Fourier transform of this function
  • Compute the discrete-space Fourier transform of this cosine

• Filter design
  • Practice question on filter design)

More Practice Problems on Digital Signal Processing (with solutions)

• Z transform
  
• Interpolation(up-sampling) and Decimation(down-sampling)
  
• DFT and FFT
  
• LTI system
  
• LTI system and filter design
  
• Properties of LTI system
  
• Describe a LTI system using Difference equation, transfer function and impulse response
  
• Periodic Convolution
  
• DFT and Periodic Convolution
  
• 2D system
  

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