Nyquist distortion

Dealing with negative frequencies and the Nyquist distortion... 

Figure 8.7 Digital Sine function - the frequency response for a zero order hold interpolator sample rate converter with L = 4, which puts the original Nyquist frequency at 0.25 7t. We can see rolloff in the passband of about -3.9 dB and very poor rejection of images outside of the passband, which result in artifacts perceived as pitch shifting distortion.

Now, if the rolloff is very gentle as is the case with an RC filter, there is an obvious problem. Since we do not want the spectral features to be distorted, the cutoff has to be set far enough from the highest frequency of interest which will be quite far away. If the Nyquist frequency is set fairly close to the spectrum of interest, the noise from that part of... 

The Nyquist plots of many real electrolyte systems deviate from the ideal Debye response, they tend to show distorted or depressed semicircles, tilted or curved spikes. The deviations can be fitted if a CPE replaces the capacitor in the equivalent circuit. A CPE is viewed as a leaky capacitor with impedance given by ... 

The question immediately arises as to the number of points required to sample the signal f t). If not enough points are taken the signal will be distorted, and if too many points are used there is a waste of resources. The answer is a remarkable result due to Nyquist given a signal with no frequency components above the signal can be completely... 

FIR filter structures can be combined very usefully with multirate processing elements. Such a filtering scheme is, however, time variant and as such may introduce some distortion during processing, but with careful design this can be minimized. Consider the design of a low-pass filter with /c = 1 /8 frequencies above this value are essentially to be eliminated. The frequency range between and the Nyquist frequency,... 

Nyquist sampling theorem A law of sampling theory stating that if a continuous bandwidth-limited signal contains no frequency components higher than half the frequency at which it is sampled, then the original signal can be recovered without distortion. 

The ADC needs at least two samples per waveform cycle in order to represent the frequency of the sound if not, then the frequency information is lost. Digital recording systems place a low-pass filter before the ADC in order to ensure that only signals below the Nyquist frequency enter the converter. Otherwise, the conversion process creates foldback frequencies, thus causing a phenomenon known as aliasing distortion (Figure 1.3). 

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