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

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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

- 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
- ADPCM

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 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

- 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

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

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

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