Wavelet Design Express VI

LabVIEW 2014 Advanced Signal Processing Toolkit Help

Edition Date: June 2014

Part Number: 372656C-01

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Owning Palette: Discrete Wavelet VIs

Requires: Advanced Signal Processing Toolkit

Designs customized analysis filters and synthesis filters for discrete wavelet analysis and reconstruction, respectively.

Dialog Box Options
Block Diagram Inputs
Block Diagram Outputs

Dialog Box Options

ParameterDescription
Wavelet TypeSpecifies the type of wavelet this Express VI uses to design a customized wavelet for discrete wavelet analysis and reconstruction. You can select the Orthogonal or Biorthogonal option.
Product of Lowpass (P0=G0*H0)Specifies P0, which is the product of the lowpass analysis filter G0 and the lowpass synthesis filter H0. Contains the following options:
  • P0 type—Specifies the type of P0. The default is Maxflat. You can choose from the following options:
    • Maxflat
    • Positive Equiripple
    • General Equiripple
    Note  The General Equiripple option is available only if you select the Biorthogonal option in the Wavelet Type section.
  • Zero pairs at pi (P0)—Specifies the value of p in the Maxflat filter P0(z), where P0(z) = (1+1/z)^(2p)*Q(z). This option is available only if you select the Maxflat option in the P0 type section.
  • # of taps—Specifies the number of coefficients of P0(z). The length of P0(z) must be 4p–1, where p = 2, 3, …. This option is available only if you select the Positive Equiripple or General Equiripple option in the P0 type section.
  • Passband—Specifies the normalized cutoff frequency of P0(z). The value of Passband must be less than 0.5. Passband is available only if you select the Positive Equiripple or General Equiripple option in the P0 type section.
Factorization (Type of G0)Contains the following options:
  • Filter type—Specifies how this Express VI factors P0 to G0 and H0. Contains the following options:
    • Arbitrary—Specifies that no restriction exists on the placement of zeros.
    • Minimum Phase—Specifies that the zeros of G0 are located inside the unit circle, except for the zeros at pi.
    • Linear Phase—Specifies that if one zero belongs to G0(H0), the reciprocal of that zero must belong to G0(H0).
    • B-Spline—Specifies that except for some zeros at pi, all the zeros of P0 belong to H0.
  • Zeros at pi (G0)—Controls how many zeros at z=–1 belong to G0(z). This option is available only if you select the Maxflat option in the P0 type section. The maximum value of this option is 2p, where p = the value of the Zero pairs at pi (P0) option.
Zeros of G0 and H0Shows the distribution of the zeros of P0(z), G0(z) and H0(z). This Express VI uses this distribution to factor the zeros of P0(z) into the zeros of G0(z) and H0(z). Because the filter coefficients of P0(z) are real, all the zeros of P0(z) are symmetrical with respect to the x-axis. Consequently, this Express VI displays only the upper half of the plane. The zeros on the x-axis represent real-valued roots. The zeros outside of the x-axis represent complex-valued roots.

The blue crosses represent the zeros of G0(z), and the red circles represent the zeros of H0(z).

Click on the zero you want to select to switch the zero from that of G0(z) to that of H0(z) and vice versa. All the zeros belong to G0(z) or H0(z).

Selecting different values for Filter type puts different constraints on the selections of zeros. For example, if you select Linear Phase for Filter type and select a zero for one filter, the filter automatically contains the reciprocal of the zero.
Wavelet and Filter BanksDisplays the following graphs:
  • Analysis scaling—Displays the scaling function of the analysis filter bank.
  • Analysis wavelet—Displays the mother wavelet of the analysis filter bank.
  • Analysis lowpass (G0)—Displays the coefficients of the lowpass analysis filter G0(z).
  • Analysis highpass (G1)—Displays the coefficients of the highpass analysis filter G1(z).
  • Synthesis scaling—Displays the scaling function of the synthesis filter bank.
  • Synthesis wavelet—Displays the mother wavelet of the synthesis filter bank.
  • Synthesis lowpass (H0)—Displays the coefficients of the lowpass synthesis filter H0(z).
  • Synthesis highpass (H1)—Displays the coefficients of the highpass synthesis filter H1(z).
Frequency responseDisplays the magnitude of the frequency responses of the designed filters G0(z) and G1(z). G1(z) is the sign-alternated version of H0(z). In other words, G1(z) is a highpass filter if H0(z) is a lowpass filter. This VI shows the frequency response of G0(z) in blue and shows the frequency response of G1(z) in green. The units of the y-axis are in dB, and the units of the x-axis are in terms of the normalized frequency. The full scale ranges from 0.0 to 1.0 pi.

Block Diagram Inputs

ParameterDescription
error in (no error)Describes error conditions that occur before this node runs.

Block Diagram Outputs

ParameterDescription
Analysis filtersReturns the coefficients of the analysis filters.
  • lowpass—Contains the coefficients of the analysis lowpass filter G0(z).
  • highpass—Contains the coefficients of the analysis highpass filter G1(z).
Analysis scalingReturns the scaling function of the analysis filter bank.
Analysis waveletReturns the mother wavelet of the analysis filter bank.
error outContains error information. This output provides standard error out functionality.
Synthesis filtersReturns the coefficients of the synthesis filters.
  • lowpass—Contains the coefficients of the synthesis lowpass filter H0(z).
  • highpass—Contains the coefficients of the synthesis highpass filter H1(z).
Synthesis scalingReturns the scaling function of the synthesis filter bank.
Synthesis waveletReturns the mother wavelet of the synthesis filter bank.

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