Spectrum analyzer with multiple operational modes

A spectrum analyzer comprising:

• means for defining a finite frequency band of interest which starts at a non-zero frequency;
• means for providing a sequence of digital words f(n), where n = 1, 2, ..., N, which correspond to samples of an analog signal at a sampling rate at least twice the upper limit of said band;
• means for combining each of said digital words f(n) with a first and a second trigonometric function, said functions being in quadrature with respect to each other and having arguments determined by the center frequency of said band and the order of the digital work f(n) in the sequence, to form respective first and second sequences of resulting digital words g(n) and h(n);
• means for digitally filtering the sequences of digital words g(n) and h(n) in accordance with a filter function determined by the width of said band to form respective sequences g(m) and h(m), where m = 1, 2, ..., M and M is less than N;
• a discrete Fourier transform processor and means for applying thereto the digital word sequences g(m) and h(m) to form thereby a set of discrete Fourier transform terms RG' and IG' from each word g(m) and RH' and IH' from each word h(m), a set of terms being formed from each of the words g(m) and h(m) for each of a selected plurality of spectral lines, where R designates the real term and I the imaginary term of a discrete Fourier transform;
• means for combining the like named terms for each subscript m to form respective discrete Fourier transform terms RG, IG, RH and IH for each spectral line;
• means for algebraically combining the terms RG, IG, RH and IH with each other to form a set of terms RU and IU representing the discrete Fourier transform of the upper half of said band translated about zero center frequency and a set of terms RL and IL representing the discrete Fourier transform of the lower half of said band translated about zero center frequency, and means for algebraically processing said terms RU, IU, RL and IL to form power spectrum values for each of said spectral lines.

A method of carrying out spectrum analysis in a selected one of a first and a second analysis mode, said first mode including processing digital samples representing the time history of an analog signal to derive power spectrum values for each of a plurality of spectral lines uniformly distributed over a frequency range starting at or about zero frequency, and said second mode including deriving power spectrum values for spectral lines distributed only within a frequency range that does not start at zero frequency, said second mode comprising the steps of:

• defining a finite frequency band of interest which starts at a non-zero frequency;
• providing a sequence of digital words f(n), where n = 1, 2, ..., N, which correspond to samples of an analog signal at a sampling rate taking into account the upper limit of said band;
• combining each of said digital words f(n) with a first and a second trigonometric function, said functions being in quadrature with respect to each other and having arguments determined by the center frequency of said band and the order of the digital word f(n) in the sequence, to form respective first and second sequences of resulting digital words g(n) and h(n);
• digitally filtering the sequences of digital words g(n) and h(n) in accordance with a filter function determined by the width of said band to form respective sequences g(m) and h(m), where m = 1, 1, ..., M and M is less than N;
• performing discrete Fourier transform processing of the digital word sequences g(m) and h(m) to form thereby a set of discrete Fourier transform terms RG' and IG' from each word g(m) and RH' and IH' from each word h(m), a set of terms being formed from each of the words g(m) and h(m) for each of a selected plurality of spectral lines, where R designates the real term and I the imaginary term of a discrete Fourier transform;
• combining the like named terms for each subscript m to form respective discrete Fourier transform terms RG, IG, RH, and IH for each spectral line;
• and
• algebraically combining the terms RG, IG, RH and IH with each other to form a set of terms RU and IU representing the discrete Fourier transform of the upper half of said band translated about zero center frequency and a set of terms RL and IL representing the discrete Fourier transform of the lower half of said band translated about zero center frequency, and algebraically processing said terms RU, IU, RL and IL to form power spectrum values for each of said spectral lines.

A spectrum analysis method comprising the steps of:

• defining a finite frequency band of interest which starts at a non-zero frequency;
• providing a sequence of digital words f(n), where n = 1, 2, ..., N, which correspond to samples of an analog signal at a sampling rate at least twice the upper limit of said band;
• combining each of said digital words f(n) with a first and a second trigonometric function, said functions being in quadrature with respect to each other and having arguments determined by the center frequency of said band and the order of the digital word f(n) in the sequence, to form respective first and second sequences of resulting digital words g(n) and h(n);
• digitally filtering the sequences of digital words g(n) and h(n) in accordance with a filter function determined by the width of said band to form respective sequences g(m) and h(m), where m = 1, 2, ..., M and M is less than N;
• carrying out discrete Fourier transform processing of the digital word sequences g(m) and h(m) to form thereby a set of discrete Fourier transform terms RG' and IG' from each word g(m) and RH' and IH' from each word h(m), a set of terms being formed from each of the words g(m) and h(m) for each of a selected plurality of spectral lines, where R designates the real term and I the imaginary term of a discrete Fourier transform;
• combining the like named terms for each subscript m to form respective discrete Fourier transform terms RG, IG, RH and IH for each spectral line;
• algebraically combining the terms RG, IG, RH and IH with each other to form a set of terms RU and IU representing the discrete Fourier transform of the upper half of said band translated about zero center frequency and a set of terms RL and IL representing the discrete Fourier transform of the lower half of said band translated about zero center frequency, and algebraically processing said terms RU, IU, RL and IL to form power spectrum values for each of said spectral lines.