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Transcript of signal and system Lecture 7
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Signals and Systems
Fall 2003
Lecture #7
25 September 2003
1. Fourier Series and LTI Systems
2. Frequency Response and Filtering3. Examples and Demos
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The Eigenfunction Property of Complex Exponentials
DT:
CT:
CT
"System Function"
DT
"System Function"
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Fourier Series: Periodic Signals and LTI Systems
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The Frequency Response of an LTI System
CT notation
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Frequency Shaping and Filtering
By choice of H(j) (or H(ej)) as a function of, we can shape
the frequency composition of the output
- Preferential amplification
- Selective filtering of some frequencies
Example #1: Audio System
Adjustable
FilterEqualizer Speaker
Bass, Mid-range, Treble controls
For audio signals, the amplitude is much more important than the phase.
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Example #2: Frequency Selective Filters
Lowpass Filters:
Only show
amplitude here.
Filter out signals outside of the frequency range of interest
low
frequency
low
frequency
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Highpass Filters
Remember:
highfrequency
highfrequency
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Demo: Filtering effects on audio signals
Bandpass Filters
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IdealizedFilters
CT
c cutofffrequency
DT
Note: |H| = 1 and H= 0 for the ideal filters in the passbands,
no need for the phase plot.
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Highpass
CT
DT
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Example #3: DT Averager/Smoother
LPF
FIR (Finite ImpulseResponse) filters
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Example #4: Nonrecursive DT (FIR) filters
Rolls off at lower
as M+N+1
increases
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Example #5: Simple DT Edge Detector
DT 2-point differentiator
Passes high-frequency components
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Example #7: A Filter Bank
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Demo: Apply different filters to two-dimensional image signals.
Note: To really understand these examples, we need to understand
frequency contents of aperiodic signals the Fourier Transform
HP
LP
BP
BP
LP
HP
Image removed do to
copyright considerations
Face of a monkey.
