starfish
Member level 2
In DSP and signal processing often we use complex exponetial representation of real signals.............what is the basic advantage we are getting from this approach??????
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Right. For any time-invariant linear system, if the input is exp(st), the output is H(s)*exp(st) for any complex s [t from -inf to inf]. The complex H(s) is the transfer function or frequency response. This is the basis of Fourier analysis.gennar said:The concept of frequency response of the system is defined using Complex exponential because if the input of the system is a complex exponenetial, the output is also a complex exp. with the same freq. but with different amp. and phase.
So, this leads to the concept of freq. response and that the output of the system is the input multiplied by the freq. response.
cesare said:Hi All,
complex number is only a convenient mathematical notation. DSP algorithms are however always implemented using conventional operations on real numbers.
Actually, I quite agree with cesare. Most dsp design is carried out in the real domain. Signals are always real. So are the filter coefficients. Complex representation only exists in dsp theory.cesare said:All the things above are true. However you cannot forget that signals in any case are "real" and all of the DSP algorithms are implemented using real number operatios.
Complex numbers are only a useful matemathical notation.