Intelligent Signal Processing Test by Angelo Ciaramella
Explore the main phases of Analog to Digital Conversion and Pulse Code Modulation in the realm of Intelligent Signal Processing. Dive into concepts like sampling theorem and more essential aspects of signal processing.
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Presentation Transcript
? Intelligent Signal Processing Test Angelo Ciaramella
Question 3 Question The sampling frequence fcof a signal with frequency band B must be ?? 2 ? ?? 2 ? ??= 2 ? ISP Verification tests .
Analog to Digital Converter x(t) xd(n) xq(n) quantizatio n sampling coding 010101 ISP Verification tests Main phases of the ADC process: sampling, quantization, coding. 3
Analog signal Amplitude (x(t)) analog signal x(t) ISP Verification tests t We start from a temporal representation of analog signal 4
Analog signal sampling samples x(t) 1 2 3 4 5 6 n ISP Verification tests Tc t We define a sampling period Tcobtaining a sampled signal xd (n) = x(nTc) 5
Pulse Code Modulation (PCM) xc(t) x(t) s(t) ISP Verification tests Pulse Code Modulation (PCM) is a mathamtical method used to digitally represent analog signals. We consider s(t) as a periodic impulse sequence obtained by (t) (delta di Dirac) 6
Pulse Code Modulation (PCM) Sampled signal xc(t) ISP Verification tests t Source signal x(t) Result of the PCM 7
Pulse Code Modulation (PCM) Impulse sequence s(t) 1 -3Tc -2T c -Tc 0 Tc 2Tc 3Tc t ISP Verification tests = ( ) ( ) ( ) xc t x t s t x(t) t Analogic signal 8
Sampling theorem The Sampling theorem defines the minimum sampling frequency which is necessary to avoid distortions in the signal reconstruction Introduced by Harold Nyquist, and appeared in 1949 in an article authored by E. C. Shannon ISP Verification tests Result Given a signal with a limited and known bandwidth, the minimum sampling frequency of this signal must be at least twice its highest frequency 9
Sampling theorem Theorem A continuous-time signal x(t) with a spectral band B strictly limited (X(f) = 0 for | f | > B) can be uniquely reconstructed from its sampled version x (n) (n = 0, 1, 2, 3, ...) if the sampling frequency fc= 1/Tcsatisfies the following relation ISP Verification tests 1 c T = B 2 f c 10
Sampling theorem x(t) t frequency domain transform ISP Verification tests X(f) frequency band B maximum frequency fmax B - 0 + theoretic f real 11
Sampling theorem X(f) x(t) frequency band B f xd(t) frequency band X(f - fc) X(f-2fc) X(f) - + ISP Verification tests . . . fc = 1/Tc 2fc f 12
Sampling theorem 2 fc B X(f) X(f+fc) X(f-fc) + fc 2fc B B f aliasing ISP Verification tests 2 B Subsampling of the signal generates aliasing 13
Sampling theorem 2 fc B X(f) X(f+fc) X(f-fc) + fc 2fc B B f no aliasing 2 B ISP Verification tests Oversampling of the signal 14
Signal recontruction X(f-fc) X(f) X(f+fc) + fc/2 -fc/2 f B -fc fc H(f) ideal low-pass filter + f B fc - B ISP Verification tests fp -fp X(f) = Xc(f)H(f) + f 15
Real filters Xc(f-fc) Xc(f) Xc(f+fc) + fc/2 -fc/2 f B -fc fc transition band H(f) + f B fc - B ISP Verification tests fp -fp guard band
Example of reconstructed signal Reconstruct signal falias = fc - f0 <f0 Source signal with frequency f0 ISP Verification tests Samples with fc < 2 f0 = f f f f alias c reale reale
References Material Slides Video Lessons Books Signal Processing Book (Ciaramella) free download on the e-learning platform Discrete-time signal processing, A. V. Oppenheim, R. W. Schafer, J.R. Buck, Upper Saddle River, N.J., Prentice Hall, 1999, ISBN 0-13-754920-2 Digital Signal Processing, J. Proakis, D. Manolakis, Prentice Hall, 4 edition, 2006 ISP Verification tests
