📄 aliasexpo.htm
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<!-- This file create by Bob L. Sturm Sept 02 2003, using vi. Originally inspired by the MATLAB Auditory Demonstrations package created by Univ. of Sheffield, UK.--><HTML><HEAD> <TITLE>SSUM: Audio Aliasing Explorer</TITLE> <link href="style.css" rel="stylesheet" type="text/css"></HEAD><BODY><table cellpadding=0 cellspacing=0 align=center border=0 width="100%"><tr> <td> <IMG SRC="aliasexpo_t.jpg" WIDTH=137 HEIGHT=146> </td> <td align=center> <H1>Audio Aliasing Explorer</H1> </td></tr><tr> <td colspan=2 align=center bgcolor=black> <H6><A HREF="#introduction">Introduction</A> <A HREF="#demonstration">Demo</A> <A HREF="#investigate">Investigate</A> <A HREF="#reading">Reading</A> <A HREF="#credits">Credits</A> <A HREF="SSUM.htm">Home</A></H6> </td></tr></table><br><A NAME="introduction"></A><H2>Introduction</H2><p>This application allows to user to simulate the effects of aliasing in audio. Aliasing occurs when a signal is sampled at a frequency too low tocapture the highest frequencies in that signal. For instance, sampling a 1000Hz tone with a sampling rate (Fs) of 10000 Hz would be able to capture thenecessary number of samples per period of the waveform in order to allowperfect reconstruction. In this case there would be 10 samples captured foreach period of the waveform. If however the Fs were 1000 Hz, then only onesample per period would be captured at the same phase position--which wouldlook like a DC offset, or straight line. If the Fs were 750 Hz, then the signaloriginally at 1000 Hz, would reappear at 250 Hz! (These effects can also bevisually demonstrated with the <a href="samplexpo.htm">Sampling Explorer</a>.)</p><br><A NAME="demonstration"></A><H2>The tool</H2><P>This tool is similar to the <a href="fourierexpo.htm">Fourier Explorer</a>, inthat is lets you move a window across the data to watch the Fourier spectrum.The bottom left plot is the time domain plot of the loaded signal. The two redbars represent a window, which you can drag across the signal. The spectrum ofthe windowed segment is computed and displayed in the top left plot.The scroll bar at the top of the spectrum plot changes the range of frequenciesdisplayed. The scroll bar to the left scales the amplitudes displayed</p><br><CENTER><a href="aliasexpo.jpg"><IMG SRC="aliasexpo.jpg" width=630 height=337></a></CENTER><br><p>Once you have loaded a signal you can choose to downsample it, thereby reducingthe effective Fs. This is done with the menu at the upper right. In the aboveexample I have loaded a 10 kHz sine wave, sampled at 44.1 kHz. I thendownsampled it by 2 (throwing away every other sample), which makes theeffective Fs = 22,050 Hz. That is still adequate for perfect reconstruction,but as can be seen the alias of the tone is moving closer to the Nyquistfrequency--shown by the red line at 11,025 Hz.</p><br><A NAME="investigate"></A><H2>Things to investigate</H2><p> <OL> <LI>In the image above, why does it appear the alias is folding over? Whatfrequency is the alias at? <LI>What will the frequency become of this tone with a downsamplingfactor of 3, 4, and 10? <LI>Load the sound "OldManPurple.wav", and choose a downsample factor of 5.Why does it still sound good? What parts of the speech can you hear thefolding? Why? <LI>Repeat the same process for the sound "clarinet.wav"? Why is there sucha difference at a factor of 5?</OL></p><A NAME="reading"></A><H2>Further reading</H2><p></p><br><H2>Credits</H2><P> The code to make the slidable window and updated spectrum was taken andimproved upon from the <a href="http://www.dcs.shef.ac.uk/~martin/MAD/docs/mad.htm">MAD</a> program "wavspect."</p><hr noshade><br><p class="credits">Produced by Bob L. Sturm and Dr. Jerry Gibson<br>Release date: January 21, 2004<br>Copyright 2004 University of California, Santa Barbara</p></BODY></HTML>⌨️ 快捷键说明
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