3-SYSC5602-time discrete signal

3-SYSC5602-time discrete signal - Digital Signal Processing

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Digital Signal Processing SYSC5602_DT_signals&sequences_2009.fm MOHAMMED EL-TANANY, PROFESSOR SYSTEMS & COMPUTER ENGINEERING, CARLETON UNIVERSITY, OTTAWA, ONTARIO 1 / 23 Discrete Time Signals and Sequences ( Read Sections 2.1-2.2 and 2.3.2 in Proakis and Manolakis) Typical DSP System Anti-alias analog Filter Quantizer Digital Signal Processor D/A Converter Output analog filter analog analog Hold A/D Converter every T Functional Diagram for a simple DSP System Removes higher frequencies to prevent aliasing Acts as a signal post-conditioner Runs desired DSP Algorithms
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Digital Signal Processing SYSC5602_DT_signals&sequences_2009.fm MOHAMMED EL-TANANY, PROFESSOR SYSTEMS & COMPUTER ENGINEERING, CARLETON UNIVERSITY, OTTAWA, ONTARIO 2 / 23 Types of Signals time Amplitude Analog : Continuos time/ Continuous amplitude time Sampled Analog: Discrete time/ Continuous amplitude T s time Sampled data: similar to sampled analog, except the samples have non-zero width T s τ
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Digital Signal Processing SYSC5602_DT_signals&sequences_2009.fm MOHAMMED EL-TANANY, PROFESSOR SYSTEMS & COMPUTER ENGINEERING, CARLETON UNIVERSITY, OTTAWA, ONTARIO 3 / 23 time Amplitude DAC output: Continuous time/ Discrete amplitude T s time Digital: Discrete time/ Discrete amplitude T s Anti-alias analog Filter Quantizer DSP D/A Converter Output analog filter analog analog Hold A/D Converter every T sampled analog Sampled data digital
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Digital Signal Processing SYSC5602_DT_signals&sequences_2009.fm MOHAMMED EL-TANANY, PROFESSOR SYSTEMS & COMPUTER ENGINEERING, CARLETON UNIVERSITY, OTTAWA, ONTARIO 4 / 23 Sequences A sampled sequence is obtained by sampling an analog signal, x(t), every T second interval. T is known as the sampling period is known as the sampling frequency . The resulting sampled sequence is of the form: For convenience, the sampling period may be dropped; in this case 1 T -- xnT () x 2 T xT x 0 x 2 T x 3 T ,, , ,,, {, } = xn x 2 x 1 x 0 x 1 x 2 x 3 , ,,,,, } = t (continuous) x(t) n (integer) x(n) 0 1 2 3 ..........
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Digital Signal Processing SYSC5602_DT_signals&sequences_2009.fm MOHAMMED EL-TANANY, PROFESSOR SYSTEMS & COMPUTER ENGINEERING, CARLETON UNIVERSITY, OTTAWA, ONTARIO 5 / 23 Basic Sequences Unit Impulse Sequence Unit Step Sequence or δ n () 1 n equal 0 0 otherwise = δ n 00010000 ,,,,,,,, {, } = -3 -2 -1 0 1 2 3 n δ (n) or un 1 n 0 0 = 00011111 } = -3 -2 -1 0 1 2 3 n u(n)
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Digital Signal Processing SYSC5602_DT_signals&sequences_2009.fm MOHAMMED EL-TANANY, PROFESSOR SYSTEMS & COMPUTER ENGINEERING, CARLETON UNIVERSITY, OTTAWA, ONTARIO 6 / 23 Constant sequence Linear Sequence xn () Af o r n ≤≤ = x(n) -3 -2 -1 0 1 2 3 n An for n = x(n) -3 -2 -1 0 1 2 3 n
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Digital Signal Processing SYSC5602_DT_signals&sequences_2009.fm
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3-SYSC5602-time discrete signal - Digital Signal Processing

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