Audio signals.html (3208B)
1 <?xml version="1.0" encoding="UTF-8"?> 2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3 <html><head><link rel="stylesheet" href="sitewide.css" type="text/css"><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/><meta name="exporter-version" content="Evernote Mac 7.5.2 (457164)"/><meta name="altitude" content="-0.9381439089775085"/><meta name="author" content="Alex Balgavy"/><meta name="created" content="2017-10-31 10:14:23 +0000"/><meta name="latitude" content="52.33479884700187"/><meta name="longitude" content="4.866838046268644"/><meta name="source" content="desktop.mac"/><meta name="updated" content="2017-12-19 19:32:31 +0000"/><title>Audio signals</title></head><body><div><span style="font-weight: bold;">Representation</span></div><div>patterns of variations that represent/encode information</div><div><br/></div><div>expressed in terms of waves — sinusoidal, sawtooth, triangle, square</div><div>waves have period, amplitude, frequency, wavelength</div><div><br/></div><div>period: T (sec)</div><div>frequency: 1/T (per sec)</div><div>wavelength: velocity/frequency (m)</div><div><br/></div><div><span style="font-weight: bold;">As functions</span></div><div>a function of time and volume (amplitude) — time t => s(t)</div><div>continuous if there is a volume for each point in time</div><div><br/></div><div>speech is one-dimensional — only changes in time</div><div>an image is two-dimensional — has x and y</div><div><br/></div><div><span style="font-weight: bold;">Digitisation of signals</span></div><div>real signals are analog signals that are continuous in all dimensions</div><div>a computer has limited space and can’t process them</div><div>therefore, digitise — sampling + quantisation</div><div><br/></div><div>Sampling</div><div><ul><li>has period/frequency, result in samples at specific points in time</li><li>x axis is now discrete</li></ul><div><br/></div></div><div>Quantisation</div><div><ul><li>representation of real numbers with finite numbers of bits</li><li>the more bits, the more information you can store</li></ul><div><br/></div></div><div><span style="font-weight: bold;">Converting analog and digital</span></div><div>analog to digital converter (ADC) — converts from analog (continuous) to digital (discrete) signal</div><div>takes input analog and reference voltage, outputs the fraction of input voltage in reference voltage</div><div><br/></div><div>digital-to-analog converter — ‘reconstruction'</div><div><br/></div><div><span style="font-weight: bold;">Digital representation</span></div><div>Ts — sampling period</div><div>fs — sampling frequency</div><div>a discrete signal is represented by a sequence of samples s[n]</div><div><br/></div><div>s[n] = s(nTs)</div><div><br/></div><div><span style="font-weight: bold;">Shannon (Nyquist) theorem</span></div><div>the sampling rate must be at least twice the highest frequency</div><div>the highest useful frequency from an FFT is half of the sampling frequency</div><div>if it’s not obeyed and your sample rate is too low, you get aliasing (false data)</div><div><br/></div></body></html>