Basic funda of Digital Signal Processing….

September 21, 2012

Generally speaking most of the signals are analog, and dealing with analog is pretty hard and becomes cumbersome at times. So to make our lives simpler these analog signals are converted into digital signals for carrying out processing in digital form. By processing I mean performing specific operations on the signal according to the requirement. After processing, signal can be reconverted back to analog form if needed.

Filter is the most important system in DSP. Filter as the name suggests will filter out the unwanted noise from the signal to be processed. They specifically remove the unwanted frequency signals thereby enhancing the required signals. There are many types of filters, the most widely used ones being the linear filters…. we start with an analog low pass pre-filter or anti-aliasing filter which limits the highest signal frequency to ensure freedom from aliasing… if the highest frequency component in a signal is fmax, then the signal should be sampled at the rate of atleast 2fmax for the samples to describe the signal completely. Basically aliasing is when components of the analog signals at high frequencies appear at lower frequencies in the sampled signal. This happens if the sampling rate is less than 2f (which is called the nyquist rate). Next we need is a sampler which operates above this nyquist sampling rate. Sometimes input signal contains unknown frequencies greater than fs. A low pass filter (anti-alias filter) after the sampler that filters all f above fmax followed by sampling at fs>2*fmax, will avoid aliasing.

Conversion of analog to digital is done with the help of something known as ADC (Analog to Digital Convertor). Here is where the concept of resolution comes into picture. For example if we have a 10bit ADC module with us, this would mean that the given analog signal will be cut into 2^10 i.e. 1024 equally spaced partitions, each having some part of the analog signal. Hence this ADC has a resolution of 10bits. Every analog signal when digitized needs to be quantized (rounded off) so we need a quantizer which would round off the signal values to a finite number of levels. This rounding off is done for each partition. Thus more the resolution, better will be the approximation.

Once we have the discrete numbers with us, we can go ahead and encode them (signal values) to a string of binary bits whose length is determined by the number of quantization levels of our quantizer….

Now comes the main part- the digital processing system itself (i.e. hardware and software) which will process the encoded digital signal in a desired fashion…the heart of the system is the digital processor which is usually based on general purpose microprocessor such as the Motorola MC68000, a digital signal processor chip such as the Texas Instruments TMS320C50, or some other piece of hardware. The digital processor implements one of the several DSP algorithms, for example digital filtering, mapping the input, x (n), into the output, y (n).

After the processing has been done, we need to produce back the new analog output. For that a decoder is usually used that converts the processed bit stream to a desired discrete signal (still discontinuous) with quantized signal values. Now to make it continuous a reconstruction filter is used that reconstructs a staircase approximation of the discrete time signal….. this analog looking signal is then fed to a low pass analog anti-imaging filter, which extracts the central period from the periodic spectrum, removes the unwanted replicas and results in a smooth reconstructed signal…..


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