Collectively solved 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 invertible? New! Waiting for input!
  • Is the following system invertible? New! Waiting for input!
  • Is the following system invertible? New! Waiting for input!
  • Is the following system invertible? New! Waiting for input!
  • Is the following system invertible? New! Waiting for input!
  • Is the following system stable?
  • Is the following system memoryless?
  • Is the following system causal?
• Linearity and time invariance of a system
  • Is the following system time-invariant?
  • Is the following system linear?
• Linearity and time invariance
  • Is the following system time-invariant?
  • Is the following system linear?
  • Is the following system time-invariant?
• 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]
  • Compute the DT Fourier transform of a sinc
  • Compute the DT Fourier transform of a rect
• 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
• Nyquist theorem
  • What is the Nyquist rate for this signal?
  • What is the Nyquist rate for this other signal?
  • Samping and reconstruction of sinc function.
  • Samping and reconstruction of sinc function multiplied by exponential.
  • Samping and reconstruction of sinc function multiplied by exponential (another one).
  • Samping and reconstruction of sinc function multiplied by exponential (another one).
  • Samping and reconstruction of sinc function multiplied by acosine.
  • What is the Nyquist rate of a sinc function multiplied by itself?
  • What is the Nyquist rate of the multiplication of two sinc functions?
• Modulation
  • Demodulation of signal modulated with exponential
  • Demodulation of signal modulated with cosine
• Z-transform
  • Computation of the z-transform
  • Another computation of the z-transform
  • Computation of the inverse z-transform
  • Another computation of the 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
  • Compute this z-transform
  • Compute this z-transform

Problems from the official textbook (Oppenheim WIllsky)

• 4.1_ECE301Fall2008mboutin
• 4.2_ECE301Fall2008mboutin
• 4.3_ECE301Fall2008mboutin
• 4.4_ECE301Fall2008mboutin
• 4.5_ECE301Fall2008mboutin
• Discussion about problem 5.31

More Practice Problems

• Example of computation of Fourier series coefficients for CT signal
• Computing the energy and power of a CT signal: two examples
• A mistake NOT TO REPEAT when computing Fourier transforms
• Laplace transform example
• Fourier transform problem
• How NOT to take a Fourier transform
• Frequency and impulse response from diff. eq.
• Example of CT convolution
• Is this system time-invariant?
• practice problems (mostly on Fourier transform)
• Finale exam practice (written by a student)

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