| Signal Processing Blockset™ | |
Delay input by time-varying fractional number of sample periods
Signal Operations
dspsigops
The Variable Fractional Delay block delays each element of the N-D input array, u, by a variable (possibly noninteger) number of sample intervals.
The block computes the value for each channel of the output based on the stored samples in memory most closely indexed by the Delay input, v, and the interpolation method specified by the Mode parameter. In Linear Interpolation mode, the block stores the D+1 most recent samples received at the In port for each channel, where D is the Maximum delay. In FIR Interpolation mode, the block stores the D+P+1 most recent samples received at the In port for each channel, where P is the Interpolation filter half-length.
See the Variable Integer Delay block for further discussion of how input samples are stored in the block's memory. The Variable Fractional Delay block differs only in the way that these stored sample are accessed; a fractional delay requires the computation of a value by interpolation from the nearby samples in memory.
When the input is sample based, the block treats each element of the N-D input array, u, as an independent channel. The input to the Delay port, v, must either be an N-D array of the same size and dimension as the input u, or be a scaler value, such that 0 ≤ v ≤ D.
For example, consider an M-by-N input matrix. Each of the Mi*N matrix elements are treated as independent channels. The input to the Delay port can be an Mi-by-N matrix of floating-point values in the range 0 ≤ v ≤ D that specifies the number of sample intervals to delay each channel of the input, or it can be a scalar floating-point value, 0 ≤ v ≤ D, by which to equally delay all channels.
A 1-D vector input is treated as an Mi-by-1 matrix, and the output is 1-D.
The Initial conditions parameter specifies the values in the block's memory at the start of the simulation in the same manner as the Variable Integer Delay block. See the Variable Integer Delay block reference page for more information.
When the input is frame based, the block treats each of the N input columns as a frame containing Mi sequential time samples from an independent channel.
The input to the Delay port, v, contains floating-point values in the range 0 ≤ v ≤ D that specify the number of sample intervals to delay the current input. The input to the Delay port can be a scalar value to uniformly delay every sample in every channel. It can also be a column-based length-M vector, containing one delay for each sample in the input frame(s). The set of delays contained in the vector is applied identically to every channel of a multichannel input. The Delay port entry can also be a row-based length-N vector, containing one delay for each channel. Finally, the Delay port entry can also be an M-by-N matrix, containing a different delay for each corresponding element of the input.
For example, if v is the Mi-by-1 matrix [v(1) v(2) ... v(Mi)]', the earliest sample in the current frame is delayed by v(1) fractional sample intervals, the following sample in the frame is delayed by v(2) fractional sample intervals, and so on. The set of fractional delays contained in v is applied identically to every channel of a multichannel input.
The Initial conditions parameter specifies the values in the block's memory at the start of the simulation in the same manner as the Variable Integer Delay block. See the Variable Integer Delay block reference page for more information.
The delay value specified at the Delay port is used as an index into the block's memory, U, which stores the D+1 most recent samples received at the In port for each channel. For example, an integer delay of 5 on a scalar input sequence retrieves and outputs the fifth most recent input sample from the block's memory, U(6). Fractional delays are computed by interpolating between stored samples; the two available interpolation modes are as follows.
For noninteger delays, at each sample time, the Linear Interpolation mode uses the two samples in memory nearest to the specified delay to compute a value for the sample at that time. If v is the specified fractional delay for a scalar input, the output sample, y, is computed as follows.
vi = floor(v) % vi = integer delay vf = v-vi % vf = fractional delay y = (1-vf)*U(vi+1) + vf*U(vi)
Delay values less than 0 are clipped to 0, and delay values greater than D are clipped to D, where D is the Maximum delay. A delay value of 0 causes the block to pass through the current input sample, U(1), in the same simulation step that it is received.
In FIR Interpolation mode, the block computes a value for the sample at the desired delay by applying an FIR filter of order 2P to the stored samples on either side of the desired delay, where P is the Interpolation filter half-length. For periodic signals, a larger value of P (that is, a higher order filter) yields a better estimate of the sample at the specified delay. A value between 4 and 6 for this parameter (that is, a 7th to 11th order filter) is usually adequate.
A vector of 2P filter tap weights is precomputed at the start of the simulation for each of Q-1 discrete points between input samples, where you specify Q in the Interpolation points per input sample parameter. For a delay corresponding to one of the Q interpolation points, the unique filter computed for that interpolation point is applied to obtain a value for the sample at the specified delay. For delay times that fall between interpolation points, the value computed at the nearest interpolation point is used. Since Q controls the number of locations where a unique interpolation filter is designed, a larger value results in a better estimate of the sample at a given delay.
Increasing the Interpolation filter half length (P) increases the number of computations performed per input sample, as well as the amount of memory needed to store the filter coefficients. Increasing the Interpolation points per input sample (Q) increases the simulation's memory requirements, but does not affect the computational load per sample.
The Normalized input bandwidth parameter allows you to take advantage of the bandlimited frequency content of the input. For example, if you know that the input signal does not have frequency content above Fs/4, you can specify a value of 0.5 for the Normalized input bandwidth to constrain the frequency content of the output to that range.
Note Each of the Q interpolation filters can be considered to correspond to one output phase of an "upsample-by-Q" FIR filter. In this view, the Normalized input bandwidth value improves the stopband in critical regions, and relaxes the stopband requirements in frequency regions where there is no signal energy. |
For delay values less than P-1, the output is computed using linear interpolation. Delay values greater than D are clipped to D, where D is the Maximum delay.
The block uses the Signal Processing Toolbox™ intfilt function to compute the FIR filters.
Note When the Variable Fractional Delay block is used in a feedback loop, at least one block with nonzero delay (for example, a Delay block with Delay > 0) should be included in the loop as well. This prevents the occurrence of an algebraic loop when the delay of the Variable Fractional Delay block is driven to zero. |
The dspaudioeffects demo illustrates three audio effects applied to a short segment of music. When you set the Audio effect of the Effect block to Flanging, the model uses the Variable Fractional Delay block to mix the original signal with a delayed version of itself. To see the Flanging subsystem, right-click the Effect block and select Look Under Mask. Next, double-click the Flanging block in the Effect block subsystem that just opened. This opens the Flanging subsystem and allows you to see the parameters of the Variable Fractional Delay block.
The method by which to interpolate between adjacent stored samples to obtain a value for the sample indexed by the input at the Delay port.
The maximum delay that the block can produce, D. Delay input values exceeding this maximum are clipped at the maximum.
Half the number of input samples to use in the FIR interpolation filter.
The number of points per input sample, Q, at which a unique FIR interpolation filter is computed.
The bandwidth to which the interpolated output samples should be constrained. A value of 1 specifies half the sample frequency.
The values with which the block's memory is initialized. See the Variable Integer Delay block for more information.
Double-precision floating point
Single-precision floating point
| Delay | Signal Processing Blockset |
| Unit Delay | Simulink |
| Variable Integer Delay | Signal Processing Blockset |
| Upsample | Variable Integer Delay | |
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