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#X text 5 294 2) Increment the frequency by some interval then count
the cycles.;
#X text 5 324 3)Repeat step two until the number of peaks starts to
decrease.;
#X text 5 354 4) Once the number of peaks starts to decrease \, the
nyquist will be somewhere in between that frequency and the last frequency
you tried. Look at the frequencies in between until you find the one
with the most peaks. This is the nyquist frequency.;
#X text 7 13 1) The table below is 0.1 second long and records at a
low enough sample rate that you won't be able to hear its output but
you'll be able to clearly see what is happening. By changing the frequency
and observing the table \, find the sampling rate.;
#X text 5 264 1) Set the frequency to 10 Hz and count the cycles of
the wave (you can do this easily by counting the peaks).;
#X restore 28 315 pd question1;
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#X msg 141 72 set \$1;
#X msg 170 10 set \$1;
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#X restore 126 71 graph;
#X text 182 77 Frequency;
#X text 182 103 Sample Rate;
#X text 136 129 Playback;
#X text 9 11 2) With a sample rate of 1000 Hz \, what is the difference
\, if any \, between sinusoidal and sinusoidal with partial signals
at frequencies of 100 Hz \, 440 Hz \, and 900 Hz? What causes this
difference or similarity?;
#X text 13 195 Directions:;
#X text 13 221 1) Set the Sample rate to 1000;
#X text 13 247 2) Set the signal type to sinusoid.;
#X text 13 273 3) Set the frequency to 100;
#X text 13 351 5) Repeat steps 2-4 with signal type Partials.;
#X text 13 377 6) Compare the two cases.;
#X text 13 403 7) Repeat steps 2-6 for 440 Hz and 900 Hz.;
#X text 13 299 4) Wait for the new sample to be recorded then play
the resampled version by clicking the sampled button under Playback.
;
#X restore 28 340 pd question2;
#X text 8 220 To access the patch for;
#X text 8 242 a question \, click the;
#X text 8 264 appropriate box below.;
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#X text 10 9 Sampling Theorem;
#X text 10 30 This patch demonstrates sampling. Of course \, we're
already digital since we're using a computer \, but we can examine
the problems of sampling by downsampling from 44.1kHz (standard cd
rate) to a lower sampling rate.;
#X text 10 90 The first question shows a graph af a very short snipped
of a waveform. It is low enough at a low sampling rate to make the
effect of sampling visible. In addition to being able to visibly find
the nyquist frequency and from it the sampling rate \, you will be
able to see the effect of sampling on amplitude.;
#X text 10 176 The second and third question allow you to hear the
difference between a sound and a sampled version of that sound. You
can set the source signal to either a single sinusoid or a sinusoid
with four harmonic partials of successively lower amplitudes (for a
total of five harmonic sinusoids). Question 2 lets you hear the effects
of wrap-around \, or aliasing. Question 3 demonstrates how aliasing
is avoided.;
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#X text 124 115 Frequency;
#X text 124 136 Sample Rate;
#X text 231 119 Playback;
#X text 75 164 Filter;
#X text 13 233 Directions:;
#X text 13 254 1) Set the signal type to partials.;
#X text 13 275 2) Pick a sample rate and a frequency below the nyquist
frequency whose partials lie above the nyquist frequency (frequency
of 440 with a sampling rate of 1000 works).;
#X text 13 322 3) With the filter turned off \, wait for the new recording
to be made then play the recording.;
#X text 13 356 4) Turn the filter on \, wait for the new recording
to be made \, then play the recording.;
#X text 13 390 5) Compare your results.;
#X text 13 7 3) In this patch \, you can turn on and off a filter that
filters the signal with a cutoff at the nyquist rate before sampling.
What happens when a signal with partials is filtered before sampling
with a cutoff at the nyquist frequency and how does this compare to
the signal with no filter?;
#X restore 28 364 pd question3;
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#X text 6 2 Interface Help;
#X text 30 23 Bang;
#X text 31 89 Toggle;
#X text 52 169 Number Box;
#X text 35 371 Slider;
#X text 11 41 A bang is a button that has no state (see toggle) and
is used to trigger something. Clicking on one should do whatever the
label next to it says.;
#X text 11 109 A toggle is a button that has state (it either has an
X in it or it does not). Toggles are often used as on/off switches
\, with an X indicating that something has been turned on.;
#X text 11 193 A number box lets you set values. You can enter things
into a number box in two ways. The easiest way to enter a specific
number is to click in the box \, type the desired number \, then press
return. If would like to scroll through settings \, you can click in
the box and move the mouse up or down while holding down the (left)
button. This will scroll through by ones. To scroll through by hundredths
\, hold down the shift key while scrolling. If a box won't let you
scroll below or above a particular number \, it has been set not to
let you slide past that number for some reason. Wile you can probably
type the number in and have it work \, it might be a bad idea \, since
the boundary was put there for a reason.;
#X text 34 404 the slider bar up or down to change its value.;
#X text 34 390 Sliders work a lot like number boxes. Click and drag
;
#X restore 28 388 pd help;