Download Introduction to Signal Processing by Sophocles Orfanidis PDF

By Sophocles Orfanidis

This ebook differs from the classical DSP ebook version pioneered by means of O/S. comprises chapters on DFT, Z-Transform and filter out layout. The e-book begins out with what one reviewer calls "fun topics", and DSP applications".

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Here, we derive this result and also consider practical reconstructors. Analog reconstruction represents some sort of lowpass filtering of the sampled signal. This can be seen in Fig. 1, where practical reconstruction has been accomplished by filling the gaps between samples by holding the current sample value constant till the next sample. This is the staircase or sample/hold reconstructor. ^ y(t) ^ y(t) T D/A staircase reconstructor ya (t) ya (t) T t t sampled signal reconstructed signal Fig.

In the notation of Eq. 18), it will be given as function of frequency by AX (f )= α log2 f fmax + β log2 f fmax = γ log2 f fmax where we have normalized the attenuation to 0 dB at f = fmax . This is the mathematical expression of the statement that the total attenuation will be γ dB per octave. By the even symmetry of the spectra, we have x = AX (fstop )= AX (fs − fmax ). Thus, the requirement that x ≥ A gives the condition AX (fs − fmax )≥ A ⇒ γ log2 fs − fmax fmax ≥A Solving this as an equality gives the minimum acceptable rate fs .

SAMPLING AND RECONSTRUCTION b(m, M)= 4 ∞ π 0 e−mx − e−(M−m)x dx 1 − e−Mx Looking this integral up in a table of integrals [30], we find: b(m, M)= 4 M cot mπ M The desired coefficients A, B, C are then: π A = b(1, 4)= cot =1 4 B = b(1, 8)= π 1 cot 2 8 C = b(3, 8)= 1 3π cot 2 8 = √ = 2+1 2 √ 2−1 2 The above results generalize to any sampling rate fs = M Hz, where M is a multiple of 4. ,(M/2)−1 The coefficients b(m, M) tend to the original Fourier series coefficients bm in the continuoustime limit, M → ∞.

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