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Unformatted text preview: j/2 This is the same as negating the frequency. As the frequency of a sine increases past its Nyquist rate, it wraps around to negative frequency. EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly 31 Minimizing Aliasing Once a signal has been sampled, there is no way to eliminate aliasing (unless we have some other information about the signal). Aliasing is minimized by ﬁrst lowpass ﬁltering the signal, then sampling: f (t ) f¯(t ) h(t ) −!0 /2 !0 /2 × !T (t ) f (t ) h(t ) −!0 /2 !0 /2 Lowpass or Anti-aliasing Filter EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly f¯(t ) t = nT Sampler 32 Any practical anti-aliasing ﬁlter will not be identically zero outside of its passband. Some aliasing will always occur. By bandlimiting with the anti-aliasing ﬁlter, we are choosing to distort the signal in a known way. This is usually preferable to sampling the non-bandlimited signal, and having unknown artifacts from aliasing. Bandlimiting also suppresses noise. EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly 33 Fourier Series and Fourier Transforms Frequency domain representation of signals simpliﬁes signal processing, • Convolution becomes multiplication • Spectral representation makes signal content easier to understand • Modulation/demodulation • Sampling Often, Fourier transforms are the only tool you will need. Some problems involve signals that don’t have Fourier transforms, like increasing exponentials (ﬁnance, populations, dynamic systems). For these we need a more powerful tool. EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly 34...
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This note was uploaded on 09/28/2013 for the course EE 108b taught by Professor Mukamel during the Fall '13 term at Singapore Stanford Partnership.

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