A binary word is a fixedlength sequence of bits 1s and 0s. Optimized product quantization 1 optimized product quantization tiezheng ge, kaiming hey, qifa ke, and jian sun abstractproduct quantization pq is an effective vector quantization method. The dynamic range of fixedpoint values is less than floatingpoint values with equivalent word sizes. Therefore, in this paper we present a complete set of simulink 6 models, which allow us to perform exhaustive behavioral simulations of any pll taking into account most of the nonidealities, such as fractionaln sigmadelta quantization noise, phase frequency detector pfd delay times and dead zones, chargepump mismatches, current. Jun 19, 2009 for each, the quantizer can additionally be constrained to have symmetrically spaced levels. Quantization, in mathematics and digital signal processing, is the process of. You construct a quantizer object to specify the quantization parameters to use when you quantize data sets. Simulink modeling and design of an efficient hardware. The essence of pq is to decompose the highdimensional vector space into the. Simulink based timedomain behavioural simulator with a statistical optimizer for the automated highlevel synthe sis of. Scalar quantizer decoder, convert each index value into. For a vector quantizer using 2 bsample, multicarrier transmission yields an improvement in signaltodistortion ratio that lies between 0. Comparing optimized and nonoptimized dpcm parameters. The block diagram used for the vehicle suspension optimizer is shown in figure 8.
Finding an optimal solution to the above problem results in a quantizer sometimes called a mmsqe minimum meansquare quantization error solution, and the resulting pdf optimized nonuniform quantizer is referred to as a lloydmax quantizer, named after two people who independently developed iterative methods to solve the two sets of. Pdf modeling of sigmadelta modulator nonidealities in matlab. Image quantization with halfprecision data types matlab. For quantization, the options are to round to the nearest representable value or to the value furthe. A smooth input signal can take on a stairstep shape after quantization. A number of different probability density functions are supported. The g711 codec block is a logarithmic scalar quantizer designed for narrowband speech. Optimized product quantization 1 optimized product quantization. In effect, scalar quantization digitizes an analog signal. Same as input explicitly specify a default data type such as fixdt1,32,16 and then use the fixedpoint tool to propose data types for your model. Parameter underflow occurs when simulink software encounters a parameter whose data type does not have enough precision to represent the parameters ideal value because the ideal value is too small.
Pdf switched capacitor sc modulator performance is prone to various nonidealities, especially at integrator stage. Written for statisticians, physicists, and engineers in the field of digital signal processing and control, this book provides an authoritative analysis of quantization noise. The block uses a roundtonearest method to map signal values to quantized values at the output that are defined by the quantization interval. Quantization quantization levels refers to the number of different sample values that can be represented in digital quantity. Nonlinear tonetransfer curve of quantizer, showing a linear region.
As such quantization noise differs from channel noise in that it is signal dependent. Simulink scope versus dsp system toolbox time scope. Design and analysis of binary scalar quantizer of laplacian. Simulinkbased timedomain behavioural simulator with a statistical optimizer for the automated highlevel synthe sis of. Effective modelling of higher order sigma delta adc.
Optimized product quantization 1 optimized product. The lloyds function optimizes the partition and codebook according to the lloyd algorithm. Simulationbased highlevel synthesis of pipeline analogtodigital. Matlab and simulink are registered trademarks of the mathworks, inc. The algorithm has been optimized and factorized for efficient fpga. The data type defines how hardware components or software functions interpret this sequence of 1s and 0s. The adc subsystem digitizes the input analog voltage by. Once you quantize data with a quantizer object, its state values might change. Mis determinedby the budget constraint of memory space to ensure a feasible. Topics covered include the analysis of floating point round off, dither techniques, and implementation issues.
Table 1 shows the variation of snr and effective number of bits in fifth order modulator for quantization level 16. Convex optimization of a firstorder sigma delta modulator ccrma. The quantizer of figure 1 has been replaced with a sigmadelta modulator. Viterbidecoder object in the softdecision mode, the output of the demodulator needs to be quantized. The quantizer block discretizes the input signal using a quantization algorithm. The quantization error, q is a random variable and will have its sample values.
Pdf optimized parametric vector quantization of speech. The main purpose of noiseshaping is to reshape the spectrum of quantization noise so that most of the noise is filtered out of the relevant frequency band, for example, the audio band for speech applications. The design of a multibit quantization sigmadelta modulator nadia. For the system shown in page 10, calculate theoretically. When x is a cell array, each numeric element of the cell array is quantized. Choose the scope based on your application requirements, how the blocks work, and the default values of each block. Quantization to fixedpoint and integer data types, casting between data types cast between data types, and use the quantize function to quantize data according to a quantizer objects specifications. To avoid overflow and minimize quantization errors, fixedpoint numbers must be scaled. The main pane of the scalar quantizer decoder block dialog appears as follows. All property values are set to defaults when you construct a quantizer object this way. Multiplying the analog voltage by 2565 with the gain block.
Quantize and encode floatingpoint input into integer output. Adaptive quantization we can adapt the quantizer to the statistics of the input mean, variance, pdf forward adaptive encoderside analysis divide input source in blocks analyze block statistics set quantization scheme send the scheme to the decoder via side channel backward adaptive decoderside analysis adaptation based on quantizer. A listing of all the properties of the quantizer object q you just created is displayed along with the associated property values. This value is a good compromise between short word lengths and a small ber penalty. When you input multiple index values into this block, the block outputs a matrix of quantized output vectors. Table 1 shows the variation of snr and effective number of bits in fifth order modulator for quantization. Understand sd toolbox 2 simulink and adapt to your system 23. Rounding the value to integer floor with the quantizer block. When pdf is even symmetric about its mean, the quantizer is to be designed for. The block accepts one input sample at a time, and provides an option for programmable coefficients.
In rounting,a numerical value is replacing by another value that is approximately equal but in truncation a. See quantizer object properties for more details to copy a quantizer object, use assignment. The data type of the index values input at port i can be uint8, uint16, uint32, int8, int16, or int32. Each step of the design process involves using the lloyd algorithm to calculate codebook values and quantizer boundary points. Identify your residual signal and reflection coefficients. The output signal taken from the simulink model is y, the cars vertical displacement. Pdf joint design of a channeloptimized quantizer and.
Optimized product quantization for approximate nearest. The discrete fir filter hdl optimized block models finiteimpulse response filter architectures optimized for hdl code generation. You can use the quantize function to quantize data according to a quantizer objects specifications. Action for out of range index value use this parameter to determine the blocks behavior when an input index value is out of range, where 0. With the fixedpoint designer software, you can select a fixedpoint data type whose scaling is defined by its binary point, or you can select an arbitrary linear scaling that suits your needs. The example goes on to quantize the training data itself. It also enables the optimization of the overall wireless. Simulink makes it easy to edit and change equation parameters using the to, and, from workspace blocks. When x is a structure, each numeric field of x is quantized.
One bit quantization has dominated in modulators due. It provides a hardwarefriendly interface with input and output control signals. The original image is displayed in the leftmost column, and the result is displayed with fixedpoint, halfprecision, and singleprecision data types. Rao, fellow, ieee abstracta computationally efficient, high quality, vector msvq 3 and splitvq 4 which employ suboptimal quantization scheme based on a parametric probability density. Pdf optimized parametric vector quantization of speech line. This process maps inputs in a different range of values to a different common value. When x is a numeric array, each element of x is quantized. The set of inputs and outputs of a quantizer can be scalars scalar quantizer. In digital hardware, numbers are stored in binary words. After you have specified the quantization parameters, the block performs an iterative process to design the optimal scalar quantizer. The matlab simulink file we provide on the attached floppy demonstrates. Behavioral modeling of rf front end devices in simulink. For given input, find index of nearest codeword based on euclidean or weighted euclidean distance measure.
We define our optimization problem in section 2, but first we give some background. The block outputs the zerobased index of the associated region. G711 codec, quantize narrowband speech input signals. Optimized product quantization product quantization involves decomposing the ddimensional vector space into m subspaces, and computing a subcodebookfor each subspace. The vector quantizer decoder block associates each input index value with a codeword, a column vector of quantized output values defined in the codebook values parameter. Use the simulink to draw the characteristic of a quantizer having the following io relation. The dpcmopt function creates these optimized parameters, using the sawtooth signal x as training data. Pdf receiver only optimized semihard decision vq for noisy. Limiting the output to a maximum of 255 the largest unsigned 8bit integer value with the saturation block.
Comparative table is drawn showing the fifth order sigma delta modulator snr value and effective number of bits for different osr at quantization level 16, with optimized zeros. Viterbidecoder object with a softinputwordlength of 3. Multiply input by constant simulink mathworks india. The scalar quantizer encoder block maps each input value to a quantization region by comparing the input value to the quantizer boundary points defined in the boundary points parameter. If you have a simulink and a dsp system toolbox license, you can use either the simulink scope or dsp system toolbox time scope. Rao, fellow, ieee abstracta computationally efficient, high quality, vector msvq 3 and splitvq 4 which employ suboptimal quantization scheme based on a parametric probability. To avoid overflow conditions and minimize quantization errors, fixedpoint numbers must be scaled. Find vector quantizer codeword that corresponds to given, zerobased index value. The saturation block produces an output signal that is the value of the input signal bounded to the upper and lower saturation values. Given m, the optimal bi and yi that minimize mse satisfy. Kaiming he2 qifa ke3 jian sun2 1university of science and technologyof china 2microsoft research asia 3microsoft research silicon valley abstract product quantization is an effective vector quantization approach to compactly encode highdimensional vectors. The section optimize quantization parameters describes how to use training data with the lloyds function to help find quantization parameters that will minimize signal distortion this section describes similar procedures for using the dpcmopt function in conjunction.
Conceptual block diagram of an optimization based 6 m synthesis tool. Notice that the mean square distortion here is much less than the distortion in the. This example shows the effects of quantization on images. Optimized product quantization tiezheng ge, kaiming he, qifa ke, and jian sun abstractproduct quantization pq is an effective vector quantization method. The output of the block is the quantized output values. Narrowband speech is defined as a voice signal with an analog bandwidth of 4 khz and a nyquist sampling frequency of 8 khz. Apply quantizer object to data matlab quantize method. Discretize input at given interval simulink mathworks. Pdf this paper describes a tool that combines an accurate. A product quantizer can generate an exponentially large codebook at very low memorytime cost. Effective modelling of higher order sigma delta adc using. Pdf pdf optimized parametric vector quantization of speech. When parameter underflow occurs, casting the ideal nonzero value to the parameters data type causes the modeled value to become zero. In rounting,a numerical value is replacing by another value.
The simulation result shows that multibit quantizer modulator can get very high snr, and based on this. One way to produce partition and codebook parameters easily is to optimize. This paper proposes a new receiver optimized semiharddecision vector quantization shdvq for noisy channels, as a technique to alleviate the drastic increase in distortion incurred when the. Scalar quantization is a process that maps all inputs within a specified range to a. The data type of the codebook values input at port c can be double, single, or fixedpoint. Pdf matlabsimulinkbased highlevel synthesis of discrete.
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