Blackman Window Generator

Overview

Blackman Window

The Blackman taper is a type of window function that gradually tapers the amplitude of a signal towards the window’s edges. It is often used in digital signal processing to smooth a signal (smoothing discontinuities at the edges of sampled signals) or to reduce spectral leakage. The Blackman window has a wider main lobe and lower level side lobes than other windows. It is named after Robert Blackman, who first described it in 1958.

The formula for the Blackman window is:

w(n) = 0.42 - 0.5 * cos(2pi*n/(N-1)) + 0.08 * cos(4pi*n/(N-1))

Aside from its common use as a window function, the Q DSP library also utilizes the blackman window generator for modulating the audio signal and generating complex envelopes.

Include

#include <q/synth/blackman_gen.hpp>

Declaration

struct blackman_gen
{
            blackman_gen(duration width, float sps);

   float    operator()();
   void     config(duration width, float sps;
   void     reset();
   void     midpoint();
};

Expressions

blackman_gen is a model of Generator. In addition to valid expressions for Generator, blackman_gen allows these expressions.

Notation

g

Object of type blackman_gen.

w

Object of type duration.

sps

Floating point value representing samples per second.

Constructor

Expression Semantics

blackman_gen(w, sps)

Construct blackman_gen given window width, w, and samples per second, sps.
C++ brace initialization may also be used.

Mutators

Expression Semantics

g.config(w, sps)

Set the window width, w, with samples per second, sps.

g.reset()

Set the current phase to the start of the window.

g.midpoint()

Set the current phase to the middle of the window.

Ramp Generators

Two subclasses of blackman_gen are specialized for ramp generation:

  1. The Blackman upward ramp generator generates a rising curve with the shape of the first half of a Blackman window taper.

  2. The Blackman downward ramp generator generates a falling curve with the shape of the second half of a Blackman window taper.

Declaration

struct blackman_upward_ramp_gen : blackman_gen
{
            blackman_upward_ramp_gen(duration width, float sps);

   void     config(duration width, float sps);
};

struct blackman_downward_ramp_gen : blackman_gen
{
            blackman_downward_ramp_gen(duration width, float sps);

   void     reset();
   void     config(duration width, float sps);
};

Expressions

blackman_upward_ramp_gen and struct blackman_downward_ramp_gen : blackman_gen ` are a models of `Ramp and implements all valid expressions of Ramp.