Apparatuses for measuring high speed signals and methods thereof

A method of measuring a high speed signal by use of a high speed measuring apparatus comprising a plurality of Analog-Digital converters (AD converter), the method comprising:

• determining an active band, on which energy exists, in the input signal;
• determining a sampling frequency of one of the plurality of AD converters;
• calculating sampling frequencies of remaining AD converters of the plurality of AD converters such that a number of overlaps of the active band is minimized and a number of coset samples acquired from the input signal is maximized;
• merging samples that are sampled at the determined and calculated sampling frequencies and output by the plurality of AD converters;
• converting the merged samples into a plurality of coset samples that each has a sampling period corresponding to a least common multiple of sampling periods of the plurality of AD converters;
• and
• reconstructing the input signal from the plurality of coset samples.

A method of measuring a high speed signal by use of a high speed measuring apparatus comprising a plurality of Analog-Digital converters (AD converter), the method comprising:

• determining different sampling frequencies of the plurality of AD converters;
• merging samples that are sampled at the determined sampling frequencies and output by the plurality of AD converters;
• modeling a linear equation configured to reconstruct an input signal from the merged samples by use of a resolution-enhanced discrete Fourier transform (DFT) frame;
• and
• reconstructing the input signal from the linear equation by use of Basis Pursuit based on L1 minimization.

An apparatus for reconstructing an input signal, the apparatus comprising:

• a plurality of Analog-Digital converters (AD converter) configured to receive the input signal, to sample the input signal at different frequencies, and to output results of the samples;
• a plurality of frequency synthesizers configured to provide the AD converters with different sampling frequencies;
• and
• a signal processor configured to receive the output results of the samples and to reconstruct the input signal.