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
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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