Signals and systems practice problems list - Rhea

Practice Problems for Signals and Systems (ECE301)

A list of collectively solved practice problems related to Signals and Systems.

• Review of complex numbers
  • Compute the magnitude of these three complex numbers
  • Compute the magnitude of these two CT signals
  • Compute the magnitude of these three DT signals
• Signal Power and Energy
  • Compute the power and energy of the following CT signal
  • Compute the power and energy of the following DT signal
• Transformation of the independent variable
  • Cascade the following time delay and time scaling
• Basic System Properties
  • Is the following system invertible?
  • Is the following system stable?
• Linearity and time invariance of a system
  • Is the following system time-invariant?
  • Is the following system linear?
• Practice problem on proving time-invariance
• Computing the output of a DT LTI system by convolution
  • Compute the output of the following DT LTI system
  • Compute the output of the following DT LTI system
  • Compute the output of the following DT LTI system
  • Compute the output of the following DT LTI system
  • Compute the output of the following DT LTI system
  • Compute the output of the following DT LTI system
  • Compute the output of the following DT LTI system
  • Compute the output of the following DT LTI system
• Computing the output of a CT LTI system by convolution
  • Compute the output of the following CT LTI system
  • Compute the output of the following CT LTI system
  • Compute the output of the following CT LTI system
  • Compute the output of the following CT LTI system
• Computing the Fourier series coefficients of a CT signal
  • Obtain the Fourier series coefficients of this CT sinusoidal
  • Obtain the Fourier series coefficients of this CT pulse-train
  • Fourier series of a square wave
  • Fourier series of |sin(pi t)|
  • A page containing several practice problems on computing Fourier series of a CT signal
• Computing the Fourier series coefficients of a DT signal
  • Obtain the Fourier series coefficients of this DT sinusoidal
  • Obtain the Fourier series coefficients of this DT pulse-train
  • A page containing several practice problems on computing Fourier series of a CT signal
• Computing the Fourier transform of a continuous-time signal:
  • Compute the Fourier transform of e^-t u(t)
  • Compute the Fourier transform of cos(2 pi t).
  • Compute the Fourier transform of cos(2 pi t + pi/12).
  • Compute the Fourier transform of a rectangular pulse-train
  • Compute the Fourier transform of a triangular pulse-train
• Properties of the Fourier transform of a continuous-time signal:
  • Derive a relationship between the FT of x(3t+7) and that of x(t)
• Computing the Fourier transform of a discrete-time signal:
  • Compute the Fourier transform of 3^n u[-n]
  • Compute the Fourier transform of cos(pi/6 n).
  • Compute the Fourier transform of u[n+1]-u[n-2]
• Causal LTI systems defined by linear, constant coefficients difference equations:
  • Example of "typical" questions on causal LTI systems defined by difference equations
  • Frequency and impulse response obtained from a difference equation describing an LTI system
  • A tricky example: only attempt if you really understand what is going on

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