Music 147 / ICS 180 / ECE 195 / ACE 277
Computer Audio and Music Programming
UCI

Because we have two ears. The listener's sense of the location of recorded sound is greatly enhanced by providing a slightly different audio signal to each ear, either by headphones or speakers.

It refers to the fact that sounds are slightly louder in one ear than in the other, due to a difference in distance of the two ears from the sound source, but probably even more significantly due to the obstructive effect of the head when the sound is off the central axis from the listener's head.

It refers to the fact that, if the sound is off the central axis of the head, a sound reaches one ear slightly later than the other ear, due to the difference in distance of the two ears from the sound source.

Approximately 345 meters/second.

0.02 ms to 0.6 ms.

Use the intended virtual location to calculate the difference in distance to the two ears. Use those distances and the speed of sound to calculate the ITD. Use the "delay~" object (or the "tapin~/tapout~" pair) to delay the signal; send the undelayed signal to one channel, and the delayed signal (delayed by the ITD) to the other channel. Note that this is really only applicable when listening with headphones. (It's unreasonable to rely on such perfect placement of speakers relative to the listener's head.)

A is propotional to 1/D.

The ratio of direct sound to reflected (reverberated) sound. When sounds are closer, the ratio of direct/reflect sound is higher.

The direction-dependent filtering effect of the pinnae.

HRTFs are a set of impulse responses (filtering functions) that correspond to the filtering effects of the pinnae, head, and shoulders from different locations. Applying the HRTF for a particular location to a sound helps make the sound seem to come from that location.

Impulses are recorded from a variety of locations equidistant from microphones placed in the "ears" of a dummy head. The resulting recordings are used as impulse responses for the HRTFs.

The simplest way is to use a "line~" object to ramp the amplitude of one speaker from 0 to 1 over the course of the sound; use 1 minus that value to control the amplitude ramp of the other speaker.

Linear panning uses the above-described method of panning, such that the over-all amplitude control on one channel is 1 minus the amplitude control imposed on the other channel. Equal-power panning uses the same method, but uses the square root of the master amplitude control value for each channel, rather than the value itself. This is comparable to panning along an arc of constant distance from the listener (by maintaining equal intensity at every point), and avoids the "hole-in-the-middle" effect sometimes caused by linear panning.

As a sound source moves toward you its perceived frequency is shifted upward by an amount determined by its velocity (relative to you) because it is, to some extent, outrunning its own sound waves. As it moves away from you, it's relative velocity is negative) so the perceived frequency is actually lowered. Thus, as a sound moves rapidly past you, the "Doppler shift" occurs (a rather sudden downward frequency shift as the relative velocity of the source goes from positive to negative). The perceived frequency can be calculated as fc/(c-v), where f is the frequency of the source sound, v is the source's velocity relative to the listener, and c is the speed of sound. Another way to calculate the Doppler effect is to delay the sound by an amount that corresponds to its virtual distance from the listener (delay equals the distance divided by the speed of sound). This requires continually calculating the source's virtual distance as it moves, and applying a continual time-variable delay to the sound.

Upward.

A low-pass filter attenuates high frequencies while allowing lower frequencies to pass through more-or-less unaltered.

A high-pass filter attenuates low frequencies while allowing higher frequencies to pass through more-or-less unaltered.

The cut-off frequency (of a high-pass or low-pass filter) is technically defined as the frequency at which the output amplitude is attenuated 3 decibels relative to the input signal. In practice, however, in the case of a resonant low-pass filter, the term "cut-off" frequency is often used in the same way as the term "center frequency" is used for band-pass filters (see below).

A band pass filter attenuates all frequencies except those that lie in a certain "passband" (range). Often a band-pass filter not only attenuates frequencies outside the specified range, but also boosts (resonates) the frequencies that lie within the passband. This is called a "resonant band-pass filter".

The bandwidth is the difference between the highest frequency of the passband and the lowest frequency of the passband. The upper and lower cut-off frequncies are defined as the frequencies at which the output amplitude is attenuated 3 decibels relative to the input signal. For example, if the amplitude drops off around 2000 Hz such that at 1800 and 2200 Hz the output amplitude is 3dB less than it was in the input signal, the bandwidth is 2200 - 1800 = 400 Hz.

The center frequency is the frequency that lies in the center of the passband of a band-pass filter (2000 Hz in the above example). In the case of a resonant band-pass filter, it is usually the frequency of greatest resonance.

For a band-pass filter, the Q is the center frequency divided by the bandwidth.

An IIR lowpass filter (see definition below) can have a variable steepness of cutoff (usually combined with resonance near the cutoff frequency. For such filters, the Q is usually calculated as if it were a band-pass filter, in which the center frequency is the frequency of greatest resonance and the "bandwidth" is equal to twice the difference between the cutoff frequency and the frequency of greatest resonance.

As the high frequencies are attenuated, the sound becomes less "bright" and more "muffled".

A resonant low-pass filter or band-pass filter will have more and more spectral emphasis around the resonant frequency as the Q is increased. The Q can be increased (i.e., the bandwidth can be sufficiently narrowed) to the point where the passband is heard as a single pitch (or narrow pitch region).

Most digital filters operate on the principle of frequency-dependent interference that occurs when a signal is combined (in varying proportions) with one or more delayed versions of itself.

The output signal is equal to the scaled input signal, plus independently scaled and delayed copies of itself, minus independently scaled and delayed copies of previous outputs:
y(n) = a0x(n) + a1x(n-1) + ... - b1y(n-1) - b2y(n-2) ...

Finite impulse response means that the filter uses a finite number of delayed copies of the input, and no copies of previous outputs. The "impulse response" is the signal created by the coefficients of each term of the input half of the filter equation. So, since the nonzero coefficients eventually come to an end in such a filter, the impusle response is finite, and when the input ceases the output the sound will go away, extended only by the duration of the impulse response.

An IIR filter feeds some copies of previous outputs back into the input of the filter (i.e., it has terms from the second half of the filter equation). As a result the output signal could potentially continue infinitely if the coefficients of the feedback copies are not small enough. (They must certainly have a magnitude less than 1, and must be even smaller if multiple feedback copies are being used.)

A comb filter has regularly-spaced (i.e. harmonic) frequencies of emphasis (separated by regularly-spaced frequencies of attenuation), such that the spectral plot of the amplitude response looks like a comb.

An FIR comb filter is achieved by combining the input signal with a scaled and delayed copy of itself. An IIR comb filter is achieved by combining the input with a scaled and delayed copy of a prior output.

The fundamental frequency is the inverse of the delay time. For example, if the comb filter uses a 1 ms delay, the filter will have amplitude peaks every 1000 Hz.

White noise is sound that has a random (and thus unpredictable but over-all uniform) distribution of amplitudes in the time domain, and of frequencies (between 0Hz and the Nyquist frequency) in the spectral domain.

By choosing discrete sample values at random.

The word "domain" refers to the x axis of the graph. A signal viewed in the time domain views amplitude as a function of time; a signal viewed in the frequency domain views amplitude as a function of the different frequencies.

A spectral plot shows the spectrum of a theoretical sound, or a single cycle of a periodic wave.

The Fourier theorem states that any periodic signal can be mathematically represented as the sum of harmonically-related sinusoids of independent amplitude and phase.

Fourier analysis is using the Fourier theorem to discover the precise frequency content (spectrum) of a sound.

The discrete Fourier transform (DFT) is a mathematical process by which a discrete time-domain signal can be converted into a corresponding discrete frequency-domain signal.

The number of discrete samples in each DFT determines the number of frequency ranges ("bins") that will be represented (between 0Hz and the sampling frequency) in the frequency-domain representation of that signal.

As the number of samples in a DFT increases, the precision of frequency resolution in the spectral plot increases. However, since a greater number of samples covers a greater period of time, the DFT will necessarily represent the average amplitude of each frequency over that period, so a DFT of a longer period might cause some "smearing" of the amplitude since a single value in the spectral plot is used to represent a (possibly varying) amplitude of each frequency range in the time-domain signal. For example, with a sampling rate of 32,768 Hz, an FFT of 128 samples covers a time period of 128/32,768=0.0039 seconds (4 ms) and yields frequency bins that cover a range of 32,768/128=256 Hz each. A DFT of 2048 samples, by contrast, would yield frequency bins of only 16 Hz (good frequency resolution) but would cover a time period of 0.0625 seconds (but a lot of variety can happen in a sound in 1/16 of a second).

A spectral plot can be re-converted into a time-domain signal using the mathematical process of the inverse DFT (IDFT). A spectral plot can be modified in many ways, however. For example, amplitudes of particular frequencies can be increased or decreased (spectral filtering), the entire plot can be multiplied by the spectrum of another signal (cross-synthesis), entire plot can be shifted up or down in frequency (frequency-shifting), the plot can be used for resynthesis of a longer or shorter time period than the original (time compression and expansion), one can perform interpoltaions between spectral plots over a certain period of time (spectral interpolation), etc.

Convolution is the process of taking one finite digital signal, scaling and delaying that signal by the amplitude and sample number of each discrete sample of another finite digital signal, and adding all those delayed-scaled copies together. It is a commutative process; i.e., convolving signal A with signal B give the same result as convolving signal B with signal A.

Convolution in one domain is exactly equivalent to multiplication in the other domain. Thus filtering is really convolution of an audio signal and an impulse response in the time domain, which would be equivalent to multiplying the DFT of the signal and the DFT of the impulse repsonse in the frequency domain.

If individual instruments, voices, and sounds are each recorded on a separate track, then each track can be independently adjusted for amplitude (to get the desired balance, or to highlight certain sounds), independently filtered (to give each sound a distinctive region of the spectrum), and processed (to give each sound its own unique, distinctive character).

Delay(s) can be used to add a comb filtering effect, a "slapback" blurring of the attack, discrete echo effects, reverberation, call-and response effects, chorusing, flanging, etc.

Time-varying delay. The delay time is modulated by some control source, such as a low-frequency oscillator, creating subtle (or not-so-subtle) Doppler effects. When a flanged sound is mixed with the unflanged original, a time-varying interference (modulated comb filtering) occurs.

The "chorus effect" is achieved by adding multiple slightly detuned versions of a signal together, emulating the slightly-out-of-tune effect of multiple voices or instruments playing in near-unison. This is most simply achieved by adding a (very slightly) delayed copy of a signal to the original, with the delay being continually varied to change its tuning slightly from the original. Unlike flanging (which is usually controlled by a periodic low-frequency control source), chorusing is usually controlled by linearly interpolated random delay times (within a very small range) so that the original and delayed signals are qlways out of tune by an unpredictably varying amount.

Reverb is added to the sound, but instead of being allowed to decay naturally, the reverb is cut off quite suddenly. This allows reverb to be used to "enrich" or "fatten" a sound, without extending its duration much. It is particularly used for percussive sounds in commercial recording. In extreme cases, the effect is almost like a burst of filtered noise.