Sixth chapter of DSP

This chapter mainly refers to the signal sampling and reconstruction, from the signal to take part of the information, and then from this part of the information to restore the original signal. Although the number of pages is not too much, but I read the two times feel labored, strands of thoughts.

6.1 Ideal sampling and reconstruction of continuous time

The sampling period is also called the sampling interval, and the reciprocal is the sampling frequency.

Non-cycle time, Fourier and I Fourier transform of discrete signals. Using NT instead of T, the Fourier transform derived from the continuous time is compared with the Fourier transform of normal discrete time, and the relationship between the sampled spectrum and the original spectrum is obtained by using some mathematical tricks. (Translational replication plus amplitude scaling), resulting in the ideal interpolation function (sinc (t/t).

Sampling theorem: With limited continuous signal, the highest frequency is b Hz, when the sampling frequency reaches 2 b sampling point per second, it can be recovered only.

The book studies the signals that have been recovered from a limited sample point for a limited period of time.

When sampling frequency is not enough, the frequency domain copy translation will affect the previous signal (a bit similar to the time domain ISI), due to the low sampling frequency, so that the translation is too little to exceed the bandwidth limit. The aliasing portion can be thought of as the original spectrum of 0.5 times times the odd number of times the sampling frequency of folding, so 0.5 times times the sampling frequency is also called the folding frequency.

When the bandwidth is less than 0.5 times times the sampling frequency, the sampled frequency corresponds to the original frequency one by one (this is equivalent to the existence of inverse function), there will be no go back.

Figure 6.1.5 The relation between the sampled signal and the time domain of the original signal.

Discrete-time signal processing for 6.2 continuous-time signals

The front filter has two functions: one is to remove the noise outside the band, and the other is to remove the high frequency component.

The continuous change is discrete, then discrete processing, and finally to a continuous.

The ideal digital-to-analog/digital converter is a time-varying system.

The ideal ADC sees no quantization error, which is equivalent to sampling only.

The spectrum of the DAC equals the spectrum of the sample sequence multiplied by the shaping spectrum. The ideal digital-to-analog converter has a function similar to window function in the frequency domain, but it can not be regarded as a filter, because the filter is the LTI system. The digital-to-analog converter is a time-varying system.

The system function of discrete time processing system can be chosen to make the whole system look at the function of the continuous time system from the black box angle.

Sixth chapter of DSP