Audio signals.md (1698B)
1 +++ 2 title = 'Audio signals' 3 +++ 4 # Audio signals 5 ## Representation 6 patterns of variations that represent/encode information 7 8 expressed in terms of waves — sinusoidal, sawtooth, triangle, square 9 10 waves have period, amplitude, frequency, wavelength 11 - period: T (sec) 12 - frequency: 1/T (per sec) 13 - wavelength: velocity/frequency (m) 14 15 ## As functions 16 a function of time and volume (amplitude) — time t => s(t) 17 18 continuous if there is a volume for each point in time 19 20 speech is one-dimensional — only changes in time 21 22 an image is two-dimensional — has x and y 23 24 ## Digitisation of signals 25 real signals are analog signals that are continuous in all dimensions 26 27 a computer has limited space and can’t process them 28 29 therefore, digitise — sampling + quantisation 30 31 Sampling 32 33 - has period/frequency, result in samples at specific points in time 34 - x axis is now discrete 35 36 Quantisation 37 38 - representation of real numbers with finite numbers of bits 39 - the more bits, the more information you can store 40 41 ## Converting analog and digital 42 analog to digital converter (ADC) — converts from analog (continuous) to digital (discrete) signal 43 44 takes input analog and reference voltage, outputs the fraction of input voltage in reference voltage 45 46 digital-to-analog converter — ‘reconstruction' 47 48 ## Digital representation 49 - Ts — sampling period 50 - fs — sampling frequency 51 52 a discrete signal is represented by a sequence of samples s[n] 53 54 s[n] = s(nTs) 55 56 ## Shannon (Nyquist) theorem 57 the sampling rate must be at least twice the highest frequency 58 59 the highest useful frequency from an FFT is half of the sampling frequency 60 61 if it’s not obeyed and your sample rate is too low, you get aliasing (false data)