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DISCRETE-SIGNAL ANALYSIS AND DESIGN- P29
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DISCRETE-SIGNAL ANALYSIS AND DESIGN- P29:Electronic circuit analysis and design projects often involve time-domainand frequency-domain characteristics that are difÞcult to work with usingthe traditional and laborious mathematical pencil-and-paper methods offormer eras. This is especially true of certain nonlinear circuits and sys-tems that engineering students and experimenters may not yet be com-fortable with.
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DISCRETE-SIGNAL ANALYSIS AND DESIGN- P29 N−1126 N := 128 n := 0, 1.. N − 1 k := 0, 1.. N − 1 VT(k) := 20⋅log 1⋅ VT(n)⋅exp −j⋅2⋅π⋅ k ⋅n ∑ N n=0 N n n V1(n) := sin 2⋅π⋅ ⋅1 V2(n) := cos 2⋅π⋅ − 0.1⋅ (rnd(1) − .5) ⋅1 VT1(k) := 0.25 VT(k − 1) + 0.5 VT(k) + 0.25 VT(k + 1) N N 2 VT2(k) := 0.25 VT1(k − 1) + 0.5 VT1(k) + 0.25 VT1(k + 1) VN(k) := VT(k) − 20⋅log(1 + k 2) VN1(k) := 0.25 VN(k − 1) + 0.5 VN(k) + 0.25 VN(k + 1) V1(n) 0 VN2(k) := 0.25 VN1(k − 1) + 0.5 VN1(k) + 0.25 VN1(k + 1) (d ) −2 −50 0 50 100 n (a) −70 VT(k) 2 −90 dB −110 VN(k) V2(n) 0 −130 −150 −2 0 20 40 60 0 50 100 k n (e) (b) −50 n VT(n) := V1(n)⋅ V2(n) − 0.5 sin 2⋅π⋅ ⋅2 N −70 VT2(k) 0.05 −90 dB VN2(k) −110 VT(n) 0 −130 −150 −0.05 0 20 40 60 0 20 40 60 k n (c) (f ) Figure 7-4 Phase noise on a test signal sine wave. THE POWER SPECTRUM 127 At the upper left is a noise-free discrete sine wave V 1 (n) at frequencyf = 1.0, amplitude 1.0, in 128 positions of (n). A discrete cosine waveV 2 (n), amplitude 1.0 at the same frequency, has some phase noise added,0.1·[rnd(1) − 0.5]. The rnd(1) function creates a random number from0 to + 1 at each position of (n). The value 0.5 is subtracted, so therandom number is then between −0.5 and +0.5. The index of the phasemodulation is 0.1. (a) The plot of the noise-free sine wave. (b) The plot of the cosine wave with the noise just barely visible. (c) We now multiply the sine wave and the cosine wave. This mul- tiplication produces the baseband phase noise output VT (n) and a sine wave of amplitude 0.5 at twice the frequency of the two input waves. We subtract this unwanted wave so that only the phase noise is visible in part (c). This is equivalent to a lowpass Þlter that rejects the times 2 frequency. Note the vertical scale in the graph of part (c) that shows the phase noise greatly ampliÞed. (d) We next use the DFT to get the noise spectrum VT (k ) in dB format. At this point we also perform ...
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DISCRETE-SIGNAL ANALYSIS AND DESIGN- P29 N−1126 N := 128 n := 0, 1.. N − 1 k := 0, 1.. N − 1 VT(k) := 20⋅log 1⋅ VT(n)⋅exp −j⋅2⋅π⋅ k ⋅n ∑ N n=0 N n n V1(n) := sin 2⋅π⋅ ⋅1 V2(n) := cos 2⋅π⋅ − 0.1⋅ (rnd(1) − .5) ⋅1 VT1(k) := 0.25 VT(k − 1) + 0.5 VT(k) + 0.25 VT(k + 1) N N 2 VT2(k) := 0.25 VT1(k − 1) + 0.5 VT1(k) + 0.25 VT1(k + 1) VN(k) := VT(k) − 20⋅log(1 + k 2) VN1(k) := 0.25 VN(k − 1) + 0.5 VN(k) + 0.25 VN(k + 1) V1(n) 0 VN2(k) := 0.25 VN1(k − 1) + 0.5 VN1(k) + 0.25 VN1(k + 1) (d ) −2 −50 0 50 100 n (a) −70 VT(k) 2 −90 dB −110 VN(k) V2(n) 0 −130 −150 −2 0 20 40 60 0 50 100 k n (e) (b) −50 n VT(n) := V1(n)⋅ V2(n) − 0.5 sin 2⋅π⋅ ⋅2 N −70 VT2(k) 0.05 −90 dB VN2(k) −110 VT(n) 0 −130 −150 −0.05 0 20 40 60 0 20 40 60 k n (c) (f ) Figure 7-4 Phase noise on a test signal sine wave. THE POWER SPECTRUM 127 At the upper left is a noise-free discrete sine wave V 1 (n) at frequencyf = 1.0, amplitude 1.0, in 128 positions of (n). A discrete cosine waveV 2 (n), amplitude 1.0 at the same frequency, has some phase noise added,0.1·[rnd(1) − 0.5]. The rnd(1) function creates a random number from0 to + 1 at each position of (n). The value 0.5 is subtracted, so therandom number is then between −0.5 and +0.5. The index of the phasemodulation is 0.1. (a) The plot of the noise-free sine wave. (b) The plot of the cosine wave with the noise just barely visible. (c) We now multiply the sine wave and the cosine wave. This mul- tiplication produces the baseband phase noise output VT (n) and a sine wave of amplitude 0.5 at twice the frequency of the two input waves. We subtract this unwanted wave so that only the phase noise is visible in part (c). This is equivalent to a lowpass Þlter that rejects the times 2 frequency. Note the vertical scale in the graph of part (c) that shows the phase noise greatly ampliÞed. (d) We next use the DFT to get the noise spectrum VT (k ) in dB format. At this point we also perform ...
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