A low-pass filter is one that leaves low frequencies unchanged, but blocks or attenuates high frequencies. Suppose a low-pass filter passes up to the 8th harmonic of a 440 Hz sound of an instrument (a musical A pitch), but it blocks all higher harmonics. How many harmonics will it pass of the A pitch one octave higher? (Remember that one pitch is an octave higher than another if the frequency of the first is double the frequency of the other.)
Remember that a ring modulator takes two signals (the higher-frequency signal is usually called the carrier, and the slower one is called the modulator) and multiplies them together. Briefly explain why, if a 500 Hz (sine wave) carrier and a 5 Hz (sine wave) modulator are combined (multiplied) by a ring modulator, the result is the same as if two (other) sine waves are added together. What are the frequencies of these other sine waves?
Remember that a ring modulator takes two signals (the higher-frequency signal is usually called the carrier, and the slower one is called the modulator) and multiplies them together. Briefly explain why, if a 500 Hz (sine wave) carrier and a 5 Hz (sine wave) modulator are combined (multiplied) by a ring modulator, the result is the same as if two (other) sine waves are added together. What are the frequencies of these other sine waves?
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8 harmonics of the lower A: 1*440 , 2*440, ... , 8*440, no higher ones will pass
The higher A is of freq, 2*440. (octave)
Its harmonics: 1*[2*440], 2*[2*440], 3*[2*440], 4*[2*440], no higher ones will pass (4*[2*440]=8*440)
So that's four.
A ring modulator multiplies to incoming signals.
multiplying two sine waves or cosines can also be rewritten using trig identities.
for example: cos(u).cos(v) = 1/2 [ cos(u-v) + cos(u+v) ]
so a 5hz wave multiplying a 500hz carrier, can also be seen/heared as two waves of 505hz and 495hz added together.
This phenomenon you hear in reverse, when two nearly but no exactly tuned flutes, are played to gether (added), you will hear a lower vibrating wave, that modulates them. (mutliplied) (sounding very shrill when really off tune). Another thing this explains: This is the reason why AM modulation in transmitters produces an upper and lower sideband....
The higher A is of freq, 2*440. (octave)
Its harmonics: 1*[2*440], 2*[2*440], 3*[2*440], 4*[2*440], no higher ones will pass (4*[2*440]=8*440)
So that's four.
A ring modulator multiplies to incoming signals.
multiplying two sine waves or cosines can also be rewritten using trig identities.
for example: cos(u).cos(v) = 1/2 [ cos(u-v) + cos(u+v) ]
so a 5hz wave multiplying a 500hz carrier, can also be seen/heared as two waves of 505hz and 495hz added together.
This phenomenon you hear in reverse, when two nearly but no exactly tuned flutes, are played to gether (added), you will hear a lower vibrating wave, that modulates them. (mutliplied) (sounding very shrill when really off tune). Another thing this explains: This is the reason why AM modulation in transmitters produces an upper and lower sideband....