Spatially variant apodization

The method of signal processing for apodization of sidelobes without widening mainlobes comprising the steps of:

• acquiring a finite set of discrete data in the frequency domain sampled at the Nyquist frequency;
• transforming the finite set of data to a space domain representation of the sampled data including one set of real data and one set of imaginary data, the transformed data having at least one mainlobe and a plurality of sidelobes associated with each mainlobe,
• for Nyquist sampled data, selecting a first limit not greater than zero or a negative value and a second limit of at least one half;
• for each set of real and imaginary data calculating a modified set of frequency domain data by
• determining weights for each sample by choosing the value of the negative of the current sample divided by the sum of the preceding sample and the following sample when that value is between the limits, at the first limit when that value is less than or equal to the first limit, and at the second limit when that value is greater than or equal to the second limit;
• determining a new value for the current sample by adding the product of the weight and the sum of the preceding sample and the following sample to the current sample;
• and
• using the waveform with attenuated sidelobes in an image-processing system.

The method of signal processing for apodization of sidelobes without widening mainlobes comprising the steps of:

• acquiring a finite set of discrete data sampled at some N integer multiple of the Nyquist frequency;
• obtaining a frequency domain representation of the sampled data including one set of real data and one set of imaginary data;
• selecting an upper limit of at least one half;
• selecting a lower limit of zero or less;
• determining weights for each real sample by choosing the value of the negative of the current sample divided by the sum of the Nth sample preceding the current sample and the Nth sample following the current sample when that value is between said limits, zero or the lower limit when that value is less than or equal to the lower limit and at the upper limit when that value is greater than or equal to said upper limit;
• determining a new value for the current real sample by adding the product of the weight and the sum of the Nth sample preceding the current sample and the Nth sample following the current sample to the current sample;
• performing the three preceding steps on the imaginary data set;
• and
• using the new real and imaginary values in an image-processing system.

The method of signal processing for apodization of sidelobes without widening mainlobes comprising the steps of:

• acquiring a finite set of discrete data which is sampled at a non-Nyquist frequency and P percent zero-padded;
• obtaining a frequency domain representation of the sampled data including one set of real data and one set of imaginary data;
• selecting a lower limit of zero or less;
• selecting an upper limit not less than the value of the following expression:
• 1/[2* sin (.pi./2-P*.pi.)];
• for each set of real and imaginary data calculating a modified set of space domain data by
• determining weights for each sample by choosing the value of the negative of the current sample divided by the sum of the preceding sample and the following sample when that value is between the lower limit and the upper limit, zero or the lower limit when that value is less than or equal to the lower limit, and at the upper limit when that value is greater than or equal to the upper limit;
• determining a new value for the current sample by adding the product of the weight and the sum of the preceding sample and the following sample to the current sample;
• and
• using the current sample in an image-processing system.

The method of signal processing for apodization of sidelobes without widening mainlobes comprising the steps of:

• acquiring a finite set of discrete data sampled at the Nyquist frequency;
• obtaining a frequency domain representation of the sampled data including one set of real data, denoted by I, and one set of imaginary data, denoted by Q;
• selecting an upper limit of at least one half for Nyquist sampled data and a lower limit of zero or less;
• determining weights for each sample by choosing the value of the expression:
• ##EQU7## denoted w(i) where I.sub.i and Q.sub.i represent the current real and imaginary components, respectively, of the current sample, I.sub.i-1 and Q.sub.i-1 represent the real and imaginary components, respectively, of the preceding sample, and I.sub.i+1 and Q.sub.i+1 represent the real and imaginary components, respectively, of the following sample;
• when that value is between the lower limit and the upper limit, zero or the lower limit when that value is less than or equal to the lower limit, and at the value of the upper limit when that value is greater than or equal to said upper limit;
• determining a modified complex value, (I'.sub.i,Q'.sub.i) for the current sample, (I.sub.i,Q.sub.i) according to the expression:
• (I'.sub.I,Q'.sub.i)=w(i)*(I.sub.i-1,Q.sub.i-1)+(.sub.i,Q.sub.i)+w(i)*(I.sub .i+1,Q.sub.i+1);
• and
• using the modified complex value in an image-processing system.

The method of signal processing for apodization of sidelobes without widening mainlobes comprising the steps of:

• acquiring a finite set of discrete data sampled at some N integer multiple of the Nyquist frequency;
• obtaining a frequency domain representation of the sampled data including one set of real data, denoted by I, and one set of imaginary data, denoted by Q;
• selecting an upper limit of at least one half for Nyquist-multiple sampled data;
• selecting a lower limit of zero or less;
• determining weights for each sample by value of the expression:
• ##EQU8## denoted w (i) where I.sub.i and Q.sub.i represent the current real and imaginary components, respectively, of the current sample, I.sub.i-N and Q.sub.i-N represent the real and imaginary components, respectively, of the Nth sample preceding the current sample, and I.sub.i+N and Q.sub.i+N represent the real and imaginary components, respectively, of the Nth sample following the current sample;
• when that value is between the lower limit and the upper limit, zero or the lower limit when that value is less than or equal to the lower limit, and the value of the upper limit when that value is greater than or equal to said upper limit;
• determining a new complex value, (I.sub.i ',Q.sub.i '), for the current sample, (I.sub.I,Q.sub.i) according to the expression:
• (I.sub.i ',Q.sub.i ')=w(i)*(I.sub.i-N,Q.sub.i-N)+(I.sub.I,Q.sub.i)+w(i)* (I.sub.i+N,Q.sub.i+N);
• and
• using the new complex value in an image-processing system.

The method of signal processing for apodization of sidelobes without widening mainlobes comprising the steps of:

• acquiring a finite set of discrete data which is sampled at a non-Nyquist frequency and zero-padded at some percentage as denoted by P;
• obtaining a frequency domain representation of the sampled data including one set of real data, denoted by I, and one set of imaginary data, denoted by Q;
• selecting a lower limit of zero or less and an upper limit not less than the value of the following expression:
• 1/[2* sin (.pi./2-P*.pi.)];
• determining weights for each sample by choosing the value of the expression:
• ##EQU9## denoted w(i) where I.sub.i and Q.sub.i represent the current real and imaginary components, respectively, of the current sample, I.sub.i-1 and Q.sub.i-1 represent the real and imaginary components, respectively, of the preceding sample, and I.sub.i+1 and Q.sub.i+1 represent the real and imaginary components, respectively, of the following sample;
• when that value is between zero and said upper limit, zero or the lower limit when that value is less than or equal to the lower limit, and the value of the upper limit when that value is greater than or equal to the upper limit;
• and
• determining a new complex value, (I.sub.i ',Q.sub.i '), for each current sample, (I.sub.i,Q.sub.i) according to the expression:
• (I.sub.i ',Q.sub.i ')=w(i)*(.sub.i-1,Q.sub.i-1)+(I.sub.i,Q.sub.i)+w(i)* (I.sub.i+1,Q.sub.i+1)
• to derive two modified sets of space domain data.

The method of signal processing for apodization of sidelobes without widening mainlobes comprising the steps of:

• acquiring a finite set of discrete complex data samples;
• obtaining a frequency domain representation of the complex data samples g(i) including real data denoted by I and imaginary data denoted by Q;
• determining weights for each sample by the expression:
• ##EQU10## selecting a lower limit w.sub.min and an upper limit w.sub.max for the weights w(i);
• determining a modified complex value g'(i) for each sample where
• g'(i)=[I(i)+jQ(i)] [1-w.sub.min /w(i)] if w(i)<w.sub.min ;
• g'(i)=0 if w.sub.min .ltoreq.w(i).ltoreq.w.sub.max ;
• and
• g'(i)=[I(i)+jQ(i)] [1-w.sub.max /w(i)] if w(i)>w.sub.max.

In a synthetic aperture radar system having an image output, the method of enhancing the image comprising the steps of:

• receiving radar signals reflected from a scene, digitizing the signals, and processing the digital signals to form a two dimensional array of image elements;
• the processing step including Fourier transforming the digital signals in two dimensions to form a complex image representation in the space domain containing main lobes and a diffraction pattern comprising side lobes;
• apodizing the complex image representation in each dimension to substantially remove the side lobes without affecting the main lobes;
• and
• generating an image from the apodized image representation.

A signal processing system for attenuating the sidelobes resulting from the transformation of a finite data sequence from the frequency domain without widening the main lobe, the system comprising:

• means for acquiring a finite set of discrete data samples in the frequency domain;
• means for transforming the set to the space domain to produce a transformed set of data samples which includes at least one mainlobe and a plurality of sidelobes;
• means for determining weights for each sample as a function of the negative of the current sample divided by the sum of the neighboring samples, where the weight is the limited to a predetermined range;
• and
• means for attenuating the sidelobes by adding to each sample the product of the determined weight and the sum of neighboring samples.