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16.362 Signal and System I The unit step response of an LTI system
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16.362 Signal and System I Linear constant-coefficient difference equations When n 1, Causality + delay
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16.362 Signal and System I Linear constant-coefficient difference equations + delay Determine A by initial condition: When n = 0, A = 1
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16.362 Signal and System I Linear constant-coefficient difference equations Two ways: (1) Repeat the procedure (2) + delay
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16.362 Signal and System I Linear constant-coefficient difference equations When t>0, Determine A by initial condition: Causality +
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16.362 Signal and System I Linear constant-coefficient difference equations Determine A by initial condition: A = 1 +
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16.362 Signal and System I Linear constant-coefficient difference equations +
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16.362 Signal and System I Fourier series representation of continuous-time periodical signal for all tPeriodic signal k is an integer form a complete and orthogonal bases Complete: no other basis is needed. Fourier series Orthogonal: Kronecker Delta
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16.362 Signal and System I Fourier series representation of continuous-time periodical signal for all tPeriodic signal k is an integer
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16.362 Signal and System I Fourier series representation of continuous-time periodical signal for all tPeriodic signal k is an integer e.g.
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16.362 Signal and System I Fourier series representation of continuous-time periodical signal 0
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16.362 Signal and System I The response of system to complex exponentials Band limited channel Bandwidth
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16.362 Signal and System I Fourier series representation of discrete-time periodical signal for all t Periodic signal
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16.362 Signal and System I Example #1
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16.362 Signal and System I Properties of discrete-time Fourier series (1) Linearity
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16.362 Signal and System I (2) Time shifting (3) Time reversal
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16.362 Signal and System I (4) Time scaling (5) multiplication
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16.362 Signal and System I (6) Conjugation and conjugate symmetry Real signal Even Real & Even
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16.362 Signal and System I (7) Parseval’s relation
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16.362 Signal and System I (8) Time difference (9) Running sum
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16.362 Signal and System I Example N = 4 [1, 2, 2, 1] [1, 1, 1, 1]
![Signal and System I Example N = 4 [1, 2, 2, 1] [1, 1, 1, 1]](http://images.slideplayer.com/33/8228882/slides/slide_21.jpg "Signal and System I Example N = 4 [1, 2, 2, 1] [1, 1, 1, 1]")
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16.362 Signal and System I Fourier series and LTI system Periodic signal System response doesn’t have to be periodic. Output periodic?
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16.362 Signal and System I
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Filtering Frequency-shaping filters Frequency-selective filters (1) Frequency-shaping filters
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16.362 Signal and System I (1) Frequency-shaping filters
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16.362 Signal and System I (2) Frequency-selective filters Low-pass high-pass band-pass
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16.362 Signal and System I Discrete-time
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16.362 Signal and System I Example: averaging
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16.362 Signal and System I Continuous-time Fourier transform Aperiodic signal k is an integer Periodic signal
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16.362 Signal and System I Continuous-time Fourier transform Aperiodic signal k is an integer Periodic signal
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16.362 Signal and System I Examples
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16.362 Signal and System I Properties of continuous-time Fourier transform (1) Linearity
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16.362 Signal and System I Properties of continuous-time Fourier transform (2) Time shifting (3) Time reversal
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16.362 Signal and System I Properties of continuous-time Fourier transform (4) Time scaling
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16.362 Signal and System I Properties of continuous-time Fourier transform (5) Conjugation and conjugate summary Real
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16.362 Signal and System I Example even Even and real
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16.362 Signal and System I Differential
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16.362 Signal and System I Integral
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16.362 Signal and System I Example
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16.362 Signal and System I Example
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16.362 Signal and System I Example
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16.362 Signal and System I Example
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16.362 Signal and System I Parseval’s relation
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16.362 Signal and System I Parseval’s relation for continuous-time Fourier series Parseval’s relation for continuous-time Fourier transfer
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16.362 Signal and System I Example 0.5 1.0 -0.5
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16.362 Signal and System I Example 0.5 1.0 -0.5
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16.362 Signal and System I Example, P. 4.14 (1) real (2) (3) Solution:
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16.362 Signal and System I Example, P. 4.14 (1) real (2) (3) Solution:
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16.362 Signal and System I Example, P. 4.14 Solution:
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16.362 Signal and System I Example, P. 4.14 (3) Solution:
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16.362 Signal and System I Example, P. 4.14 (3) Solution: (1) real
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16.362 Signal and System I Multiplication
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16.362 Signal and System I Example #1
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16.362 Signal and System I Example #2
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16.362 Signal and System I Frequency-selective filtering with variable center frequency x Low pass filter x 1
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