DSP Basics

What is DSP ?

Digital Signal Processor device which takes digital signal and alters them through different algorithms and provides the results within milliseconds. These are normally found in Speakers, Mobiles..

In audio applications, DSP plays a key role to use different features like ANC, adaptive filtering, Noise suppression..

Digital Signal Processing :

X(t) -> Anti aliasing -> Sample & hold ->  ADC -> DSP -> DAC -> Reconstructed signal -> Y(t)

Audio Processing - Modification audio within same domain 

Sampling - Converting the continuous signal into discrete signal 

Nyquist Theorem - Samples that can be reconstructed back when sampling at frequency higher than                                     the maximum frequency

Nyquist rate - Rate at which a signal can be re-constructed after sampling

                            fs >2fmax

ex: For 10khz signal will have to sampled at greater than 20khz 

                            if sampling rate > nyquist rate -> Signal oversampled

                               sampling rate < nyquist rate -> Signal undersampled also know as Aliasing

In the below figure freq = 1000 time = 0.01 sec sampling rate = 48000

No of samples present in this signal = Max-frequency * Time * Sampling frequency

                                                          = 1000 * 0.01 * 48000

                                                          = 480 samples


For one single cycle   = Max-frequency * Time * Sampling Rate 

                                   = 1000 * 0.001 * 48000

                                   = 48 samples


                    




In audacity, we can't generate a tone more than the half of the sampling frequency as shown below 



It will not generate because its not satisfying the nyquist criteria which fs > 2fmax
In the above example I'm using sampling frequency = 48K and max frequency should have be less than 24K

we will not get any waveform if it exactly Fs/2 as shown below


Even if select less than the Fs/2 also sometimes we will not get exact sine wave because theoretically nyquist rate should have to Fs > 2Fmax but practically Fs > 2.5Fmax.



Even if re-sample we will not get proper sine wave because signal already lost which we can't restore

Anti-Aliasing - pre-alias apply low pass filter to attenuate high sampled frequencies  




Quantization - Process of converting discrete time domain signal to discrete time discrete amplitude                              signal

Quantization error - Difference between quantized value & original value 




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