Fundamentals of Audio Signals

1 / 34

# Fundamentals of Audio Signals - PowerPoint PPT Presentation

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Fundamentals of Audio Signals' - jacob

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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
• 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
• 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
• 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
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
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
• 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
• 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
• 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 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 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
• The method that has been discussed for storing audio is known as pulse code modulation (PCM).
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 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 Modulation
• Other PCM topics:
• mu-law and A-law companding
• DPCM
• DM
Digital Signal Processing
• Processing of a digital signal to achieve special effects may generally be described in terms of some simple functions:
• Multiplication
• Delay
• Resampling
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 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 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 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
• 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
• 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 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 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 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 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
• 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