Signals, Digitisation and DSP

Transcription

1 C H A P T E R 1 Signals, Digitisation and DSP 1.1. INTRODUCTION Signals are generated in the real world as information relating to events of various causes whether signals are generated by us for a purpose, such as in a broadcast station, or they are gleaned from an external source, such as the ECG of the physiological origin, they need to be processed in some way or other. A simple tuned filter in a radio receiver processes the received signal by selectively tuning to the desired broadcast frequency. It does this all the time the signal is in the air and is a real-time signal processor. Consisting as it does a simple coil and a tuning capacitor, it filters out the wanted frequency and hands it over to the detector circuit for continuous listening of the broadcast at the wanted frequency. It does the wonderful job of picking the signal of that chosen frequency from the spectrum of the various frequencies that may be picked by the receiver antenna. It is an analog signal processor which does the job of a tunable band-pass filter. Using passive components of resistors, capacitors and inductors, several filters can be fabricated and that is the realm of analog filters. This subject was developed during the fifties sixties of the previous century. Subsequently, when operational amplifiers and active circuitry on a chip were developed during the late sixties, many active filter circuits were evolved to provide improved performance and to meet strict design specifications of filters. For example, with only passive components, it is not easy to design, say, a low pass filter, with sharp cutoff at the low-pass edge or with a clean flat response without any droop in the pass-band. The use of OPAs and active filter theory enabled the development of such precise filters. Those were needed in the improved communication techniques that were developed in the 1970s in line communication. Signal processing comprises generally a certain number of functions or operations which could be made on the signals to improve the desired energy components and discriminate against noise or interference which could have corrupted the signals. The main processing operations are:

2 2 A Practical Approach to Digital Signal Processing Filtering, estimation, transformation, coding and identification. Fig. 1.1 DSP deals with numbers that are samples of the signal Today, the several methods of line and radio communication that are employed to squeeze information of various kinds (voice, data, image signals etc.) and transmit all over the globe and into space, has stringent requirements in the retrieval of such signals that are processed by the equipment at the receiving end. First, signals need to be processed in specific ways particular to the type of the signal. For example, a quadrature-amplitude-modulated phaseshift-keyed (QAM-PSK) signal from a telephone modem that sends data has to be processed in circuitry that are specific to the QAM technique. Filters which have to deal with these signals are not easy to design using merely active and passive components. In digital communication, cellular telephony and satellite based mobile telephony, DSP is used. In the transmitter, by a suitable choice of the modulation, the speech signal is encoded and filtered to satisfy the low transmit bit rate in the transmit channel. At the receiver, the signal is again digitally filtered to reduce noise and adjacent-channel interferences. The digital CD (Compact Disc), the Video-phone which senses the coded images over telephony channel together with compressed voice signals, and the answering machine in digital telephone (tapless), semiconductor memory storage etc., are all typical present day DSP intensive consumer applications in communication. Can we not numerically evaluate the signal for processing it in the designed manner? If the input signal is available in numbers and if the operation of filtering or whatever processing can be written down into a mathematical formula (or algorithm), then surely one could evaluate the numbers that represent the output signal after such processing. What would this process need? Essentially, it will involve: 1. The signal at input must be converted into numbers. This must be done by taking samples of the analog signals at instants in time that are equally spaced. The more the samples that are taken per second, the better it would be, because even fine and fast variations of input signal can only then be taken care of. 2. To do the formula for finding the numeric value of the output signal, a numerical calculation has to be done. That would need a computer or similar microprocessor. 3. The numbers that are evaluated have to be done fast enough; as fast as the input samples are being collected. If the evaluation takes time, then it is required to reduce the time of sampling. That means, fast or high frequency components of a signal will be missed.

3 Signals, Digitisation and DSP 3 + Fig. 1.2 The methods of signal processing over the decades of this century (a) Passive analog filters (b) Active analog filters and (c) Digital processing of signals 4. The evaluated signals in numbers have to be transformed back into analog signal. This needs a DAC. It takes numbers and forms a voltage level in an analog fashion that represents the number. The essentials of such digital signal processing is thus shown in Fig The analog-to-digital converter (ADC) is at the front-end. The digital-to-analog converter (DAC) is at the rear end. The numbers represent signal samples from the data which are processed using a microprocessor. It needs the associated components of program memory and data memory SPEED AND RESOLUTION These are the two vital aspects of the DSP components. During the time that is available between successive samples, the calculation of the output signal must be done. For example, if samples are taken at 40,000 per second, there is a time-gap between samples of 1/40,000 or ms or 25 µs. Any calculation for the filtering or processing that is intended will have to be completed well before this 25 µs. The calculations may involve several multiplications and additions depending on the type and nature of the filter operation. Hence, unless the unit time for one multiply and add operation is itself very small, (less than 1 µs), it is not possible to perform real-time filtering.

4 4 A Practical Approach to Digital Signal Processing Another aspect is that of the digitization of the signal, or converting the signal sample into numbers. The ADC itself takes a finite time for conversion. A fast device may typically take 0.5 microsecond for conversion. A sample and hold circuit is usually employed so that the signal is held constant during the time of conversion. Fig. 1.3 A sample and hold circuit keeps the chosen sample constant for the ADC to convert correctly How finely does the ADC resolve the smallest variation of the input signal? This depends on the number of bits into which the signal is converted by the ADC. There are 8-bit devices and 12-bit devices for ADC that are common. The latter is the preferred component for DSP. The ADC itself takes time for the conversion, which can be as slow as a dozen samples per second (as in ADC bit) or as fast as 0.6 µs, with flash A/D conversion. For DSP with present-day DSP hardware, conversion time for ADc chips may be even as low as 100 nonoseconds. This means one can convent 10 million samples per second. Fig. 1.4 The number of ADC bits decide the resolution of the signal processing by DSP 1.3. SPEED OF DSP HARDWARE The digital processing of the converted samples involves: (i) the storage of the samples of data as they occur, for n samples in memory (n depends on the nature and type of filtering);

5 Signals, Digitisation and DSP 5 (ii) use of these past samples together with the current sample in evaluating the current filtered output sample, for which the formula has to be known; (iii) in the case of IIR filters, the output samples are also required to be stored (2n samples). If one attempts to use a general purpose microprocessor for doing these for a typical digital filter, this will involve several instructions. One example, which illustrates this, can be seen in Appendix 1.1, where a typical and simple low-pass filter is implemented using an For this, the time taken for one sample of output is 2µs. Hence the input samples have to be taken at a slow rate of 500-per second and the filter can be built only upto 250 Hz of audio signals. Perhaps the fast PC using 486 processor, which can work at a clock speed 30 times faster than the 8085 and can speed up or extend the filter operation upto 7.5 khz. While the present use DSP does not anyway extend beyond around 10 MHz for Video signals, the use of general purpose microprocessors do not provide the answer. 4 fast 2GHz clock PC would limit the upper frequency a typical low-pass filter to 100 khz. For doing a 1024 point fast Fourier transform in real time, the evaluations being more complex, (N log 2 N = multiplications and additions), the time consumed is so much as to limit the DSP to about 50KHz sample rate with a fast 2GHz clock. Present microelectronic DSP devices are specially tuned in their architecture to specifically cater to the speed needed for Digital Signal Processing. A review of the chips that have been produced is given later in the second chapter. Designers of these have inculcated a bit of the concept of parallelism in processing and made two operations that are independent to be processed simultaneously. (i.e., in parallel). Most of the filters in DSP need a multiplication and addition, such as ax n + bx n _ 1 where the x s are fetched from signals in memory and a, b form a table of constants. Here there are two products x n is the present sample and x n _ 1 is the past or previous sample. Operation Result 1. Load signal x n Temp. Reg. = T = x n 2. Multiply by a Product = P = ax n 3. Load, transfer and accumulator = ax n accumulate previous product x n x n 1 accumulator = ax n T = x n 1 4. Multiply by b p = bx n 1 5. Add product a = ax n + bx n 1 In operation 3, three things take place simultaneously: (i) a data movement, (ii) an addition, and (iii) a transfer between registers.