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Fundamentals of Audio Signals Two signals of different amplitudes A greater amplitude represents a louder sound. Fundamentals of Audio Signals Two signals of different frequencies A greater frequency represents a higher pitched sound. Fundamentals of Audio Signals

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fundamentals of audio signals
Fundamentals of Audio Signals
  • Two signals of different amplitudes
  • A greater amplitude represents a louder sound.
fundamentals of audio signals2
Fundamentals of Audio Signals
  • Two signals of different frequencies
  • A greater frequency represents a higher pitched sound.
fundamentals of audio signals3
Fundamentals of Audio Signals
  • Any sound, no matter how complex, can be represented by a waveform.
  • For complex sounds, the waveform is built up by the superposition of less complex waveforms
  • The component waveforms can be discovered by applying the Fourier Transform
    • Converts the signal to the frequency domain
    • Inverse Fourier Transform converts back to the time domain
sampling
Sampling
  • Sounds can be thought of as functions of a single variable (t) which must be sampled and quantized
  • The sampling rate is given in terms of samples per second, or, kHz
    • During the sampling process, an analog signal is sampled at discrete intervals
    • At each interval, the signal is momentarily “held” and represents a measurable voltage rate
quantization
Quantization
  • Audio is usually quantized at between 8 and 20 bits
    • Voice data is usually quantized at 8 bits
    • Professional audio uses 16 bits
    • Digital signal processors will often use a 24 or 32 bit structure internally
quantization6
Quantization
  • The accuracy of the digital encoding can be approximated by considering the word length per sample
  • This accuracy is known as the signal-to-error ratio (S/E) and is given by:
    • S/E = 6n + 1.8 dB
    • n is the number of bits per sample
quantization7
Quantization
  • When a coarse quantization is used, it may be useful to add a high-frequency signal (analog white noise) to the signal before it is quantized
    • This will make the coarse quantization less perceptible when the signal is played back
    • This technique is known as dithering
  • During the sampling process, an analog signal is sampled at discrete intervals
  • At each interval, the signal is momentarily “held” and represents a measurable voltage rate
channels
Channels
  • We may also have audio data coming from more than one channels
  • Data from a multichannel source is usually interleaved
  • Sampling rates are always measured per channel
    • Stereo data recorded at 8000 samples/second will actually generate 16,000 samples every second
digital audio data
Digital Audio Data
  • A complete description of digital audio data includes (at least):
    • sampling rate;
    • number of bits per sample;
    • number of channels (1 for mono, 2 for stereo, etc.)
analog to digital conversion
Analog to Digital Conversion
  • Nyquist’s theorem states that if an arbitrary signal has been run through a low-pass filter of bandwidth H, the filtered signal can be completely reconstructed by making only 2H (exact) samples per second.
  • So, a low-pass filter is placed before the sampling circuitry of the analog-to-digital (A/D) converter.
analog to digital conversion11
Analog to Digital Conversion
  • If frequencies greater than the Nyquist limit enter the digitization process, an unwanted condition called aliasing occurs
  • The low-pass filter used will require the use of a gradual high-frequency roll-off, thus a sampling rate somewhat higher than twice the Nyquist limit is often used
  • A/D conversion may make use of a successive approximation register (SAR)
analog to digital conversion12
Analog to Digital Conversion
  • The low-pass filter can cause side effects.
    • One way that these side effects can be overcome is through the use of oversampling - a signal-processing function that raises the sample rate of a digitally encoded signal.
    • Consumer and professional 16-bit D/A converters often use up to 8- and 12-times oversampling, raising the sampling rate of a CD (for example) from 44.1 kHz to 352.8 kHz or 529.2 kHz.
    • By altering the signal’s noise characteristics, it is possible to shift much of the overall bandwidth noise out of the range of human hearing.
pulse code modulation
Pulse Code Modulation
  • The method that has been discussed for storing audio is known as pulse code modulation (PCM).
pulse code modulation14
Pulse Code Modulation
  • PCM is common in long-distance telephone lines.
    • The analog signal (voice) is sampled at 8000 samples/second with 7 or 8 bits per sample
    • A T1 carrier handles 24 voice channels multiplexed together
    • The bandwidth of this type of carrier can be calculated as follows:
      • 8 bits x 8000 samples/second x 24 channels = 1.544 Mbps
    • Note that one out of 8 bits is for control, not data.
pulse code modulation15
Pulse Code Modulation
  • D/A conversion process
    • parallelize the serial bit stream
    • generate an analog voltage analogous to the voltage level at the original time of sampling
    • An output sample and hold circuit is used to minimize spurious signal glitches
    • a final low-pass filter is inserted into the path
      • Smooths out the non-linear steps introduced by digital sampling
pulse code modulation16
Pulse Code Modulation
  • Other PCM topics:
    • mu-law and A-law companding
    • DPCM
    • DM
    • ADPCM
digital signal processing
Digital Signal Processing
  • Processing of a digital signal to achieve special effects may generally be described in terms of some simple functions:
    • Addition
    • Multiplication
    • Delay
    • Resampling
digital signal processing18
Digital Signal Processing
  • Addition of two signals is accomplished by adding the sample values of the signals at each sampling point: h(t)=f(t)+g(t)
    • We can add as many signals as desired together
  • Multiplication of a given signal is represented as: g(t)=m*f(t), where m is the multiplication factor.
    • Multiplication is used to increase or decrease the gain (loudness) of a signal. If m>1, g is louder than f. If m<1, g is less loud than f
    • Note that when adding signals together or multiplying by a number greater than one, care must be taken when the signal reaches the upper limit of the sample size
digital signal processing19
Digital Signal Processing
  • Delay is an important effect described as follows: g(t)=f(t+d), where d is a delay time
    • Use delay and addition to model echo:
      • f(t) = HELLO
      • g(t) = f(t + d1) , where 0 <d1
      • g(t) = HELLO
      • h(t) = f(t + d2) , where 0 <d1 < d2
      • h(t) = HELLO
      • F(t) = f(t) + g(t) + h(t)
      • = HELLO HELLO HELLO
digital signal processing20
Digital Signal Processing
  • Now consider a more realistic echo effect. We need to make each succeeding echo softer. We can do this with multiplication.
    • g’(t) = m*g(t)h’(t) = n*h(t), 0<n<m<1
    • F’(t) = f(t) + g’(t) + h’(t)

= HELLO HELLOHELLO

digital signal processing21
Digital Signal Processing
  • When delays of 35-40 ms and greater are used, the listener perceives them as discrete delays
  • Reducing the delay to the 15-35 ms range will create delays that are too closely spaced to be perceived as discrete delays
    • When used with instruments, the brain is fooled into thinking that more instruments are playing than there actually are
    • combining several short term delay modules that are slightly detuned in time, an effect known as chorusing can be achieved (used by guitarists, e.g.)
pitch related effects
Pitch-Related Effects
  • DSP functions are available that can alter the speed and pitch of an audio program. These can:
    • Change pitch without changing duration
    • Change duration without changing pitch
    • Change both duration and pitch
  • The process for raising and lowering the pitch of a sample is shown on the next slides
noise elimination
Noise Elimination
  • The noise elimination process can be seen to consist of three steps:
    • Visual analysis
    • De-clicking
    • De-noising
  • Use visual analysis to determine the type of noise and to guide the next two steps
noise elimination26
Noise Elimination
  • De-clicking involves the removal of noise generated by analog side effects such as tape hiss, needle ticks, pops, etc.
    • This is similar to ‘snow’ removal in image processing
      • (the noise manifests itself as large discontinuities in the sample waveform)
    • The noise is likely to have affected more sample data in the audio file than in the corresponding image file
      • A needle skip which affects 1/4 second of the file affects 11000 samples at the audio CD sampling rate
      • Therefore, reconstruction of the affected area is not the straightforward linear interpolation process used in images
      • Must examine a large portion of the waveform to reconstruct
noise elimination27
Noise Elimination
  • De-noising involves the removal of background noise such as hum, buzzes, air-conditioner noises, etc
    • The waveform is analyzed to determine if louder sounds will mask the softer sound
    • This involves breaking down the audio spectrum into a large number of frequency bands
    • The signal is compared with a signature which represents the background noise. This is taken from a silent moment in the samplefile. It must be determined which portion of a signal is noise and whether the noise can be deleted without distorting the program
digital signal processing28
Digital Signal Processing
  • Other DSP functions include digital mixing and sample rate conversion
    • Digital mixing is the integration of a number of digital audio signals into a single ouput signal
  • Sample rate conversion is necessary when a signal sampled at one rate must be played back on or transferred to equipment which uses another rate
    • An example is the use of digital audio as the sound track for video. The incoming rate of 44.1 kHz must be “pulled-down” to 44.056 kHz
fading
Fading
  • Fading is another important DSP function
    • During a fade, the calculated sample amplitudes are either proportionately reduced or proportionately increased in level, according to a defined curve ramp
      • For example, usually when performing a fade out, the signal will begin at a level that is 100 percent of its current value and will reduce over the defined time to 0 percent
    • Examples of various fade curves are shown in the following slides
fading32
Fading
  • To find the linearly faded value of a sample at time tx, t0≤tx≤t1, we use the following equation:
    • s’(tx) = s(tx) * (tx - t0) / (t1 - t0)
  • We can also combine the fade in of one soundfile with the fade out of another soundfile to produce the effect known as crossfade
fading34
Fading
  • Note that the two curves intersect at 50% attenuation and that the sum of the two values at any point in time is always 100%
  • Thus, we can add together the two signals to form our crossfaded signal and the amplitude of the waveform will never be greater than the maximum possible amplitude