DSP Blockset

FIR Rate Conversion

Upsample, filter, and downsample an input signal.

Library

Filtering / Multirate Filters

Description

The FIR Rate Conversion block resamples the discrete-time input to a period K/L times the input sample period, where the integer K is specified by the Decimation factor parameter and the integer L is specified by the Interpolation factor parameter. The resampling process consists of the following steps:

• The block upsamples the input to a higher rate by inserting L-1 zeros between input samples.
• The upsampled data is passed through a direct-form II transpose FIR filter.
• The block downsamples the filtered data to a lower rate by discarding K-1 consecutive samples following each sample retained.

K and L must be relatively prime integers; that is, the ratio K/L cannot be reducible to a ratio of smaller integers. The FIR Rate Conversion block implements the above three steps together using a polyphase filter structure, which is more efficient than straightforward upsample-filter-decimate algorithms. The output of the interpolator is the first filter phase, while the output of the decimator is the last filter phase. When both K and L are greater than 1, the resulting output is the last decimation phase from the first interpolation phase.

The FIR filter coefficients parameter specifies the numerator coefficients of the FIR filter transfer function H(z).

The coefficient vector, [b(1) b(2) ... b(m)], can be generated by one of the filter design functions in the Signal Processing Toolbox (such as fir1), and should have a length greater than the interpolation factor (m>L). The filter should be lowpass with normalized cutoff frequency no greater than min(1/L,1/K). All filter states are internally initialized to zero.

Frame-Based Operation

This block accepts only frame-based inputs. An M_i-by-N frame-based matrix input is treated as N independent channels, and the block resamples each channel independently over time.

The Interpolation factor, L, and Decimation factor, K, must satisfy the relation

for an integer output frame size M_o. The simplest way to satisfy this requirement is to let the Decimation factor equal the input frame size, M_i. The output frame size, M_o, is then equal to the Interpolation factor. This change in the frame size, from M_i to M_o, produces the desired rate conversion while leaving the output frame period the same as the input (T_fo = T_fi).

Latency

The FIR Rate Conversion block has no tasking latency. The block propagates the first filtered input (received at t=0) as the first output sample.

Examples

The dspsrcnv demo compares sample rate conversion performed by the FIR Rate Conversion block with the same conversion performed by a cascade of Upsample, Digital Filter, and Downsample blocks.

Diagnostics

An error is generated if the relation between K and L shown above is not satisfied.

• (Input port width)/(Output port width) must equal the
  (Decimation factor)/(Interpolation factor).
  

A warning is generated if L and K are not relatively prime; that is, if the ratio L/K can be reduced to a ratio of smaller integers.

• Warning: Integer conversion factors are not relatively prime in 
  block 'modelname/FIR Rate Conversion (Frame)'. Converting ratio 
  L/M to l/m.
  

The block scales the ratio to be relatively prime, and continues the simulation.

Dialog Box

Interpolation factor

The integer factor, L, by which to upsample the signal before filtering.

FIR filter coefficients

The FIR filter coefficients, in descending powers of z.

Decimation factor

The integer factor, K, by which to downsample the signal after filtering.

References

Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.

Supported Data Types

• Double-precision floating point
• Single-precision floating point

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Downsample	DSP Blockset
FIR Decimation	DSP Blockset
FIR Interpolation	DSP Blockset
Upsample	DSP Blockset
fir1	Signal Processing Toolbox
fir2	Signal Processing Toolbox
firls	Signal Processing Toolbox
remez	Signal Processing Toolbox
upfirdn	Signal Processing Toolbox

See the following sections for related information:

• Converting Sample Rates and Frame Rates
• Multirate Filters
• Filtering -- List of all DSP Blockset filtering blocks

FIR Interpolation

Flip