Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Electrical signal parameter measurement system
Reexamination Certificate
2002-04-30
2004-05-04
Barlow, John (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Electrical signal parameter measurement system
C702S066000
Reexamination Certificate
active
06732058
ABSTRACT:
FIELD OF THE INVENTION
The invention relates to signal processing, and more particularly to tone detection in optical systems.
BACKGROUND OF THE INVENTION
In some detection schemes, a WDM (wavelength-division multiplexed) optical signal carrying a plurality of channels has impressed upon each of its channels a respective unique dither resulting in each channel having a unique tone. Typically, the channels are modulated via amplitude modulation resulting in AM (Amplitude Modulation) tones each having a fixed modulation depth, for example, of approximately 8%. Other modulation schemes are also used. Since the tones have a fixed modulation depth, channel power is a function of the tone power and channel power is measured by detecting the tones of fixed modulation depth. To detect the tones impressed on channels of the WDM optical signal, N time domain samples of the power of the WDM optical signal are collected at a sampling frequency, f
s
. Typically, a DFT (Discrete Fourier Transform), a radix-M FFT (Fast Fourier Transform) or any other conventional transform is performed upon the N time domain samples to produce N frequency domain samples each having a unique center frequency.
To produce N frequency domain samples from N time domain samples DFTs require a number of arithmetic operations of the order of N
2
. In comparison, a conventional radix-M FFT requires on the order of Nlog
M
(N) arithmetic operations. FFTs are therefore computationally efficient when compared to DFTs even for N as low as 100. However, a conventional radix-M FFT requires that the N frequency domain samples be computed simultaneously. Generally, only a fraction of the N frequency domain samples contain tones and as such only those frequency domain samples containing tones are required. Therefore since a portion, which can be significant, of the N frequency domain samples calculated are not required, the efficiency of the conventional radix-M FFT is compromised.
SUMMARY OF THE INVENTION
Various methods and apparatuses are provided for performing a radix-M FFT (Fast Fourier Transform) upon N time domain samples to produce N/S frequency domain samples for detecting tones of dithers impressed on channels of a WDM (wavelength Division Multiplexed) optical signal. Successive tones have a tone frequency spacing, &Dgr;f
ta
, and a sampling frequency, f
s
, is chosen so that f
s
=N&Dgr;f
ta
/S. The sampling frequency, f
s
, is also less than or equal to a maximum sampling frequency, f
s,max
, at which the time domain sample can be sampled. Center frequencies of successive frequency domain samples of the N/S frequency domain samples differ by S&Dgr;f where S is an integer given by S=M
w
with w being an integer and &Dgr;f=f
s
/N being a frequency bandwidth. The radix-M FFT is performed in k=log
M
(N) stages, r, where 1≦r≦k and within each one of the stages, r, radix-M computations are performed on data points that correspond to the N time domain samples prior to the radix-M FFT. More particularly, within a stage, r, where 1≦r≦w, N/M
r
radix-M computations are performed and within a stage, r, where w<r≦k, N/M
w+1
radix-M computations are performed. This results in a reduction in the number of radix-M computations required when compared to a conventional radix-M FFT. The methods and apparatuses may be used to measure channel power. Furthermore, the radix-M FFT may be used to operate on a sequence of 2N real valued time domain samples by re-arranging the 2N real valued time domain samples into a sequence of N complex valued time domain samples, performing the radix-M FFT upon the sequence of N complex valued time domain samples and then applying a split function to recover N/S frequency domain samples.
In accordance with a first broad aspect of the invention, provided is a method of performing a radix-M FFT (Fast Fourier Transform). M is an integer satisfying M≧2. The method involves sampling a signal, containing tones, with a sampling frequency, f
s
, to produce N time domain samples. Each time domain sample initializes a respective one of N data points, wherein N is an integer. To produce frequency domain samples having a frequency bandwidth &Dgr;f=f
s
/N and center frequencies of frequency spacing M
w
&Dgr;f with w being an integer satisfying w≧1, in a reduced number for calculation the following steps are performed. For each one of k stages wherein k=log
M
(N), radix-M computations are performed upon a respective subset of the N data points. The respective subset contains only data points upon which the frequency domain samples that contain the tones are dependent. Furthermore, the sampling frequency, f
s
, used is such that the frequency domain samples contain the tones.
In some embodiments of the invention, for a stage, r, of the k stages wherein r is an integer satisfying 1≦r≦w, N/M
r
radix-M computations may be performed upon its respective subset of the N data points. Furthermore, for a stage, r, of the k stages wherein w<r≦k, N/M
w+1
radix-M computations may be performed upon its respective subset of the N data points.
In some cases the tones may have a frequency spacing, &Dgr;f
ta
, and the sampling frequency, f
s
, may satisfy f
s
=N&Dgr;f
ta
,/M
w
.
The method may be applied to a WDM (Wavelength Division Multiplexed) optical signal having a plurality of channels. Some of the channels may each have impressed upon itself a unique dither resulting in a respective unique tone. The unique tone may have a tone frequency, f
ta
, satisfying f
ta
=a&Dgr;f
ta
+C where a is an integer and C in a positive real number. The unique tones may be detected and then converted into a power.
In accordance with another broad aspect, provided is a method of performing a radix-M FFT where M is an integer satisfying M≧2. The method includes sampling a signal, containing tones, with a sampling frequency, f
s
, to produce a sequence of 2N real valued time domain samples, wherein N is an integer. The sequence of 2N real valued time domain samples is split into two sequences of N real valued data points and the two sequences of N real valued data points are combined into a sequence of N complex valued data points. To produce frequency domain samples having a frequency bandwidth, &Dgr;f=f
s
/N, and center frequencies of frequency spacing M
w
&Dgr;f with w being an integer satisfying w≧1, the following steps are followed: 1) for each one of k stages wherein k=log
M
(N), radix-M computations are performed upon a respective subset of the sequence of N complex valued data points. The respective subset contains only data points upon which the frequency domain samples are dependent; and 2) after the radix-M FFT computations have been performed for each one of the k stages, a split function is applied only to data points of the sequence of N complex valued data points upon which the frequency domain samples are dependent. Furthermore, the sampling frequency, f
s
, is such that the frequency domain samples contain the tones.
Data points obtained from the split function which correspond to the frequency domain samples may be re-ordered using bit reversal operations.
In accordance with another broad aspect, provided is a processing apparatus which is used to perform a radix-M FFT upon N time domain samples, wherein N and M are integers with M≧2. The N time domain samples are sampled at a sampling frequency, f
s
, from a signal containing tones to produce frequency domain samples that contain the tones. The apparatus has a memory adapted to store data which include N data points each being initialized by a respective one of the N time domain samples. The apparatus also has a processor capable of accessing the memory. The processor is used to perform, for each one of k stages wherein k=log
M
(N), radix-M computations upon a respective subset of the N data points. The respective subset contains only data points upon which the frequency domain samples that contain the tones are dependent. Furthermore, the freq
Jin Dongxing
Marziliano Leonard
Remedios Derrick
Wan Ping
Barlow John
Donnelly Victoria
Tropic Networks Inc.
Washburn D.
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