Filter Design Toolbox

normalize

Normalize quantized filter coefficients

Syntax

• h = normalize(Hq)
  

Description

h = normalize(Hq) accounts for quantized filter coefficient overflow by normalizing the quantized filter coefficients in the quantized filter Hq. The new quantized filter h contains the normalized coefficients. All quantized filter coefficients for h stored in the QuantizedCoefficients property value are modified to have magnitude less than or equal to one. The result also modifies the ReferenceCoefficients property value for h accordingly. normalize also modifies the ScaleValues property value for h from that of Hq, so that input data to each section of h are scaled to compensate for the normalized filter coefficients. The scaling factors used in normalize are powers of two. There may be a different scaling factor for each section of the quantized filter. You can apply normalize to direct form IIR and FIR filters only. To apply normalize to a quantized filter, its property Hq.FilterStructure must be one of the following strings:

• 'df1'
• 'df1t'
• 'df2'
• 'df2t'
• 'fir'
• 'firt'
• `antisymmetricfir'
• 'symmetricfir'

Examples

Create a direct form II transposed quantized filter and use normalize to account for overflow.

• % Create a low pass reference filter in the Signal Proc. Toolbox.
  
  [b,a] = ellip(5,2,40,0.4);
  
  % Create the quantized filter from the reference.
  
  hq = qfilt('df2t',{b,a});
  
  Warning: 5 overflows in coefficients.
  

You are warned that some of the coefficients have overflowed. To account for this overflow, use normalize to modify the ReferenceCoefficients, QuantizedCoefficients, and ScaleValues property values for Hq.

• hq = normalize(hq)
  
  hq = 
  Quantized Direct form II transposed filter                            
  Numerator                                                             
       QuantizedCoefficients{1}    ReferenceCoefficients{1}             
    (1)       0.365295410156250  0.365289835338219130                   
    (2)       0.395721435546875  0.395708380608267300                   
    (3)       0.724884033203125  0.724891008581378560                   
    (4)       0.724884033203125  0.724891008581378120                   
    (5)       0.395721435546875  0.395708380608267240                   
    (6)       0.365295410156250  0.365289835338218350                   
  Denominator                                                           
       QuantizedCoefficients{2}    ReferenceCoefficients{2}             
    (1)       0.250000000000000   0.250000000000000000                  
    (2)      -0.541015625000000  -0.541012429707579350                  
    (3)       0.790557861328125   0.790542752251058410                  
    (4)      -0.668945312500000  -0.668930473694134720                  
    (5)       0.365966796875000   0.365965902328318770                  
    (6)      -0.103698730468750  -0.103697674644671510                  
                                                                        
     FilterStructure = df2t                                             
         ScaleValues = [0.03125  1]                                     
    NumberOfSections = 1                                                
    StatesPerSection = [5]                                              
   CoefficientFormat = quantizer('fixed', 'round', 'saturate', [16  15])
         InputFormat = quantizer('fixed', 'floor', 'saturate', [16  15])
        OutputFormat = quantizer('fixed', 'floor', 'saturate', [16  15])
  MultiplicandFormat = quantizer('fixed', 'floor', 'saturate', [16  15])
       ProductFormat = quantizer('fixed', 'floor', 'saturate', [32  30])
           SumFormat = quantizer('fixed', 'floor', 'saturate', [32  30])
  

Notice that none of the coefficients overflow, and that the ScaleValues property value has changed.

See Also
get, set

noperations

noverflows