5. FIR Filters, Problems With and Without Solutions

Block diagram of FIR system and output signal
Cascade Connection of LTI Systems
Cascade of Two LTI Systems
Commutative property of convolution
Construct Output via Linearity and Time-Invariance
Convolve discrete-time signals defined by MATLAB
Determine linearity, time-invariance and causality
Determine output using linearity and time-invariance
Determine the Duration of the Output of an FIR Filter
Determine the Output of an FIR Filter for a Given Input
Difference Equation ↔ Block Diagram of FIR Filter
Difference Equation from Block Diagram of FIR Filter
Difference equation & block diagram from impulse response
Difference equation and H(z) from impulse response
Difference equation and impulse response of cascaded LTI systems
Draw Block Diagrams from FIR Difference Equation
End points for regions of FIR filter output
Evaluate convolutions with discrete-time impulses and unit steps
Explore the Use of Linearity and Time-Invariance for FIR Filters
FIR filtering of signal defined by its spectrum
FIR filtering of signal via convolution
Find Output of FIR Filter Given Coefficients
Find Outputs of an FIR Filter for Step and Cosine Inputs
Find the Impulse Response of an FIR Filter
Impulse & step response of FIR system
Impulse Response of FIR Filter; Complex Exponential Response
Impulse response & difference equation of a cascaded system
Impulse response & difference equation of cascaded systems
Impulse response & frequency response of FIR filter
Impulse response & output signal from FIR difference equation
Impulse response & output signal from cascaded systems
Impulse response & output signal of cascaded systems
Impulse response and output of discrete-time system
Impulse response of a cascaded system
Impulse response of cascade of two systems
Impulse response of cascaded LTI systems
Length of Convolution
Length of FIR filter output
Linearity & Time-Invariance Properties
Linearity & Time-Invariance Used to Construct Output Signal
Linearity, time-invariance and causality of systems
Matching Output Signal to h[n] or Difference Equation
Matching outputs to systems with given inputs
Nonzero output regions of FIR system defined by summation
Nonzero region of FIR filter output
Nonzero regions of FIR filter output
Output and impulse response of FIR system via convolution
Output from FIR Filter for Complex Exponential Input Signal
Output from FIR Filter for Finite-Length Input Signal
Output from FIR Filter for Finite-Length Input Signal; Impulse Response
Output from FIR Filter for Finite-Length Real Exponential (Decaying)
Output from convolution of impulse response & input pulse
Output of FIR system via convolution
Output of LTI System to Complex Exponentials
Output of LTI System to Finite Length Complex Exponential
Output of LTI System to u[n]
Output signal using linearity & time-invariance
Plot Finite-Length Signal x[n] Defined by Shifted Impulses
Properties of LTI systems
Running Average FIR Filter; Step Response
Simple convolution problems with MATLAB
Step response & impulse response of FIR system via convolution
Test for Linearity and Time-Invariance
Unit step response of 3-point averager
Unit-step response of FIR system via convolution
Using the Unit Step Sequence to Represent a Finite-Length Signal


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McClellan, Schafer, and Yoder, Signal Processing First, ISBN 0-13-065562-7.
Prentice Hall, Upper Saddle River, NJ 07458. © 2010 Pearson Education, Inc.