Frequency transformation fro band pass to low pass prototype. More...

Public Member Functions
def	__init__
	Create a frequency transformation instance.
def	normFreq
	Normalize frequency to lowpass prototype.
def	unormFreq
	Unnormalize frequency from lowpass prototype.
def	unormGroupDelay
	Convert lowpass prototype group delay to unnormalized group delay.
def	normGroupDelay
	Convert unnormalized group delay to lowpass prototype group delay.

Detailed Description

Frequency transformation fro band pass to low pass prototype.

Definition at line 4071 of file libcommonfunc.py.

Constructor & Destructor Documentation

def libcommonfunc.FrequencyTransformBP.__init__	(	self,
		P
	)

Create a frequency transformation instance.

Fractional bandwidth.

Definition at line 4076 of file libcommonfunc.py.

References libcommonfunc.FrequencyTransformBP.BW, libcommonfunc.Sparameters.f0, libcommonfunc.FrequencyTransformBP.f0, libcommonfunc.Sparameters.FBW, and libcommonfunc.FrequencyTransformBP.FBW.

Member Function Documentation

def libcommonfunc.FrequencyTransformBP.normFreq	(	self,
		freq
	)

Normalize frequency to lowpass prototype.

    @param freq = Vector with frequency values to convert (in Hz). Numpy array.
    @return Vector with lowpass prototype normalized frequency values. Numpy array.

    [Cameron eq. (3.113)]:

$\omega ' = \frac{f_0}{\Delta f} \left( \frac{f}{f_0} - \frac{f_0}{f} \right)$

Definition at line 4095 of file libcommonfunc.py.

References libcommonfunc.FrequencyTransformBP.BW, libcommonfunc.Sparameters.f0, and libcommonfunc.FrequencyTransformBP.f0.

def libcommonfunc.FrequencyTransformBP.normGroupDelay	(	self,
		groupDelay
	)

Convert unnormalized group delay to lowpass prototype group delay.

    @param groupDelay = Double with unnormalized group delay (in seconds) value to convert. 
    @return groupDelay = normalized filter group delay value.

    [Cameron, eq. (3.91)]:

$\tau_{0}= \frac{2}{\Delta \omega} \tau_{0} '$

Definition at line 4157 of file libcommonfunc.py.

References libcommonfunc.FrequencyTransformBP.BW.

def libcommonfunc.FrequencyTransformBP.unormFreq	(	self,
		w
	)

Unnormalize frequency from lowpass prototype.

    @param w = Vector with normalized frequency values to convert. Numpy array.
    @return Vector with unnormalized frequency values (in Hz). Numpy array.

$\omega ' = \frac{f_0}{\Delta f} \left( \frac{f}{f_0} - \frac{f_0}{f} \right)$

$f^2 - \omega ' \Delta f f - f_0^2 = 0$

$f = \frac {\omega ' \Delta f + \sqrt{( \omega ' \Delta f)^2 + 4 f_0^2 } } {2}$

with $\omega'' = \omega' \Delta f / f_0$ :

$f = \frac {f_0}{2} \left( \omega'' + \sqrt{ \omega'' \, ^2 + 4 } \right)$

Definition at line 4126 of file libcommonfunc.py.

References libcommonfunc.Sparameters.f0, libcommonfunc.FrequencyTransformBP.f0, libcommonfunc.Sparameters.FBW, and libcommonfunc.FrequencyTransformBP.FBW.

def libcommonfunc.FrequencyTransformBP.unormGroupDelay	(	self,
		freq,
		groupDelay
	)

Convert lowpass prototype group delay to unnormalized group delay.

    @param freq = Vector with unnormalized frequency values (in Hz). Numpy array.
    @param groupDelay = Vector with lowpass prototype group delay values to convert. Numpy array.
    @return Vector with unnormalized filter group delay values (in seconds). Numpy array.

    [Cameron, eq. (3.90)]:

$\tau_{BPF}= \frac{\omega_0}{\Delta \omega} \left( \frac{1}{\omega_0} - \frac{\omega_0}{\omega^2} \right) \tau ' = \frac{1}{2 \pi \Delta f} \left( 1 + \left( \frac{f_0}{f} \right)^2 \right) \tau '$

Definition at line 4144 of file libcommonfunc.py.

References libcommonfunc.FrequencyTransformBP.BW, libcommonfunc.Sparameters.f0, and libcommonfunc.FrequencyTransformBP.f0.

The documentation for this class was generated from the following file:

libcommonfunc.py

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation