RF Design Magazine


Understanding the sampling process
Sep 1, 2004 12:00 PM  By R. N. Mutagi

Sampling is the first step in the process of converting a continuous analog signal to a sequence of digital numbers. This article provides an insight into time and frequency domains of sampled signals. The concept of the spectral window, defined by the sampling process, helps understand digital signals and signal processing.

Is digital better than analog?

This question is asked frequently as we are trying to replace analog signals and systems by digital signals and systems in recording, broadcasting, communication, measurements and many other applications. Surprising to many, the answer is ‘not always.’ If we compare the two signals at source, analog always wins. When we say, at source, we mean that no additional degradation is inserted in both the signals. However, remember that quantization always degrades the digital signal, however small that degradation may be. Using more bits per sample we may reduce this degradation to a level below our perception, however, measuring instruments can tell the difference. A most expensive digital camera cannot provide a better picture than a conventional camera. Try enlarging both pictures and you will notice the difference. Music from a CD cannot be better than the original analog music from which it is recorded. At best digital can match analog quality subjectively. Then, what is all this fuss about digital?

When signals are processed, stored or transmitted during which if they undergo some degradation then digital comes out a winner. Digital signals are more robust to noise and distortions. Digital processing has many advantages over analog signal processing. It is more economical, reliable and accurate to handle signals in the digital domain. Information can be transmitted and received at long distances more efficiently by digital means than analog under identical conditions such as transmitted power, bandwidth or terminal size. Degradation in analog systems is gradual in terms of time or external influences. Digital systems, on the contrary, provide constantly higher performance up to a point beyond which the performance falls sharply. The performance of the analog systems would have fallen below the acceptable level much before this point. That is where digital is better than analog.

Real-time processing or off-line processing?

Cost of the signal processing system is in direct proportion to the speed requirements. The decision to use DSP, microprocessor or EPLD to carry out a given task is generally based on the number of multiplications and accumulations (MACs ) required in a signal processing application. The time available for the processor to carry out the required computations in real-time is the sampling duration, T, which is the inverse of the sampling frequency fs, as shown here:

Knowing the signal frequency we choose the sampling frequency and, hence, the period. We can estimate the number of processing cycles required for a given application, such as filtering. The signal samples are supplied to the processor successively. Real-time processing is feasible from the device and if it can carry out the required computations after receiving a sample and before the next sample arrives.

In many applications a block of samples is needed before computation can begin. For example, in the Fast Fourier Transform (FFT) computations for spectral analysis, we store a block of, say 1024 samples, and then compute the FFT coefficients for the entire block. While this is being done the next block is stored in a second memory. This is called pseudo-real time computation. In off-line applications we store the required number of samples and process them leisurely for future use.

ABOUT THE AUTHOR

R.N.Mutagi holds a B.E. in Telecommunications from Karnatak University and a diploma in Electronics Design technology from the Indian Institute of Science, both from India. He worked at the Indian Space Research Organization, Ahmedabad as the head of Baseband Processing Division developing satellite communication systems. He also worked at EMS Technologies at Montreal as design manager and systems engineer. His interests include DSP, digital communications and signal compression. He has authored many articles and papers.

Mutagi can be contacted at mutagi@ieee.org.

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