FUsignal

class pylayers.signal.bsignal.FUsignal(x=array([], dtype=float64), y=array([], dtype=float64), label=[])

Bases: pylayers.signal.bsignal.FBsignal, pylayers.signal.bsignal.Usignal

FUsignal : Uniform signal in Frequency Domain

x : nd.array((1xN)) y : Complex nd.array((… x N )

symH : force Hermitian symetry –> FHsignal symHz : force Hermitian symetry with zero padding –> FHsignal align : align two FUsignal on a same frequency base enthrsh : Energy thresholding thresh = 99.99 % dBthrsh : dB thresholding thresh = 40dB ift : Inverse Fourier transform resample : resampling with a new base newdf : resampling with a new df zp : zero padding until len(x) = N plotri : plot real part and imaginary part plotdB : plot modulus in dB get : get k th ray window :

Methods Summary

applyFriis()	apply Friis factor
dBthrsh([threshdB])	dBthrsh : dB thresholding of an FUsignal
decimate([N])	decimate FUsignal by N Parameters ———- N : int decimation factor (default 2)
dftresamp(df_new)	non finished
electrical_delay(tauns)
energy([axis, Friis, mode])	calculate energy along a given axis of the FUsignal
enthrsh([thresh])	Energy thresholding of an FUsignal
get(k)	get the kth signal from the FUsignal
ifft([Npt])	Inverse Fourier transform
ift([Nz, ffts, beta])	Inverse Fourier Transform - returns the associated TUsignal
iftshift([Nz])	Return the associated TUsignal
info()	Display Information about the FUsignal
newdf(df)	resample the FUsignal using phase and module interpolation
show(**kwargs)	imshow visualization of Modulus and Phase
symH([parity])	enforce Hermitian symetry
symHz(Nz[, scale])	Force Hermitian symmetry with zero padding
tap(**kwargs)	calculates channel taps
zp(N)	zero padding until length N

Methods Documentation

applyFriis()

apply Friis factor

The Friis factor is multiplied to y

\[ \begin{align}\begin{aligned}y := \( \frac{-j c}{4 \pi f} \) y\\x is frequency in GHz\end{aligned}\end{align} \]

boolean isFriis is set to True

dBthrsh(threshdB=40)

dBthrsh : dB thresholding of an FUsignal

decimate(N=2)

decimate FUsignal by N Parameters ———- N : int

decimation factor (default 2)

dftresamp(df_new)

non finished

df_new :

electrical_delay(tauns)

energy(axis=-1, Friis=False, mode='mean')

calculate energy along a given axis of the FUsignal

axis : (default 0) Friis : boolean mode : string

mean (default) | center | integ | first | last

>>> ip = TUsignal()
>>> ip.EnImpulse()
>>> En1 = ip.energy()
>>> assert((En1>0.99) & (En1<1.01))

If Friis is true energy is multiplied by

\(\frac{-j*c}{4 pi fGHz}\)

axis = 0 is ray axis

if mode == ‘mean’

\(E=\frac{1}{K} \sum_k |y_k|^2\)

if mode == ‘integ’

\(E=\delta_x \sum_k |y_k|^2\)

if mode == ‘center’

\(E= |y_{K/2}|^2\)

enthrsh(thresh=99.99)

Energy thresholding of an FUsignal

threshfloat

threshold in percentage (default 99.99)

EMH2 : cumul energie H

get(k)

get the kth signal from the FUsignal

k : indes to get

G : FUsignal

ifft(Npt=-1)

Inverse Fourier transform

Nptint

default -1 (same number as x)

tc : TUsignal

\[x = \textrm{linspace}(0,\frac{1}{\delta f},N)\]

\[y = [0,\mathbb{X}_u^T]\]

ift(Nz=1, ffts=0, beta=0)

Inverse Fourier Transform - returns the associated TUsignal

Nz : Number of zeros (-1) No forcing ffts : 0 (no fftshift 1:fftshift) beta : kaiser window shape

0 : rectangular 5 : similar to a Hamming 6 : similar to a Hanning 8.6 : similar to a blackman

uh :

>>> from pylayers.signal.bsignal import *
>>> e = TUsignal()
>>> e.EnImpulse()
>>> E  = e.fft()
>>> EU = E.unrex()

1 - Force Hermitian symmetry –> FHsignal with or without zero padding 2 - Inverse Fourier transform with or without fftshift

FHsignal.ifft, FUsignal.symH, FUsignal.symHz

iftshift(Nz=1)

Return the associated TUsignal

apply the inverse fftshift operator to come back in time

info()

Display Information about the FUsignal

newdf(df)

resample the FUsignal using phase and module interpolation

df

U : FUsignal

show(**kwargs)

imshow visualization of Modulus and Phase

vmin : vmax : cmap : colormap

symH(parity=0)

enforce Hermitian symetry

parityinteger

0 even 1 odd

V : FHsignal

symHz(Nz, scale='extract')

Force Hermitian symmetry with zero padding

Nzint

Number of zero above f[-1]

scalestring

default : ‘extract’ | ‘cir’

SH : FHsignal

The signal is rescaled in order to conserve energy

Let denotes the FUsignal as \(mathcal{X}_d\) The Fourier matrix is :math:`left[ matrix{mathbb{1}\

mathbb{W}_d\ mathbb{W}_u}right]`

FHSignal

>>> N     = 11
>>> x     = np.linspace(2,11,N)
>>> y1    = sp.randn(N)+1j*sp.rand(N)
>>> y2    = sp.randn(N)+1j*sp.rand(N)
>>> y1[0] = 0
>>> y2[0] = 0
>>> y     = np.vstack((y1,y2))
>>> S     = FUsignal(x,y)
>>> FH =  S.symHz(10)

tap(**kwargs)

calculates channel taps

fcGHzfloat

center frequency GHz

WGHzfloat

bandwidth GHz

Ntap : number of taps baseband : boolean

default : True

htapi

[Tse] David Tse, http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter2.pdf page 26

zp(N)

zero padding until length N

N : int

FUsignal