L4-Quantisation

L4-Quantisation - 1 Amplitude Quantisation Sampling of an...

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Unformatted text preview: 1 Amplitude Quantisation Sampling of an analog signal, such as voice, will produce signal samples, which have continuous range of amplitudes. In other words, each signal sample is represented by an infinite number of amplitude levels. However, human hearing can detect only finite intensity differences. As a result, it is only necessary to approximate the original analog signal with signal samples of finite number of amplitude levels. The process of transforming the sample amplitude ) ( s nT m of an analog message signal ) ( t m at time s nT t = into a discrete amplitude ) ( s nT y taken from a finite set of possible amplitudes is called amplitude quantisation. The device used for quantisation is often referred to as the quantiser. Here, it is assumed that the quantisation process is memoryless and instantaneous . This means that the transformation of the sample amplitude at time s nT t = is not affected by earlier or later samples of the message signal. Consider a memoryless quantiser as shown: The signal amplitude m is specified by the index k if it lies inside the amplitude interval L k m m m Q k k k ,..., 2 , 1 }, { : 1 = < + , where L is the total number of amplitude levels used in the quantiser. The amplitudes m k , k=1,2,,L , are called decision levels or decision thresholds. The output amplitudes y k k=1,2,,L are called the representation levels or reconstruction levels. The interval between two adjacent representation levels is called a quantum or step size. Quantiser g ( m ) Continuous sample m ( nT s ) Discrete sample y ( nT s ) m k-1 m k y k m k+1 m k+2 Q k 2 A quantiser may be classified as: Linear or uniform representation levels are uniformly spaced. Nonlinear or nonuniform representation levels are not equally spaced. Also, a quantiser may be characterised as either midtread or midrise type: Example: Uniform quantiser of the (a) midtread and (b) midrise type. Note: Once quantised, the instantaneous values of the analog signal can never be restored exactly. This gives rise to random error variations, which are signal dependent, called quantisation distortion or quantisation noise . Preferred term as this type of uncertainty is signal dependent, and can be regarded as a high order form of signal distortion. Commonly used in textbooks (noise is strictly not signal dependent). 4 3 2 1 -1 -2 -3 -4 1 2 3 4 -4 -3 -2 -1 Output level Intput level Midrise 4 3 2 1 -2 -3 -4 1 2 3 4 -4 -3 -2 -1 Output level Intput level Midtread 3 Quantisation distortion is defined as the difference between the input signal m and the quantised output signal y , given by y m q = or m y q = The quantisation distortion can be made as small as desired by increasing the number of quantising levels (i.e., to reduce the quantising step size)....
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This note was uploaded on 05/09/2011 for the course ENGR 601 taught by Professor Kah-chung during the Three '11 term at Curtin.

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L4-Quantisation - 1 Amplitude Quantisation Sampling of an...

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