Abstract: A method according to which a discrete waveform is multiplied by a sine function having an arbitrary period. The product is summed over a selected interval to derive a first summation and multiplied by a cosine function having the same period and the product is summed over the interval to provide a second summation. The sine and cosine functions are multiplied together and the product is summed over the interval to provide a third summation. The sine function is squared and summed over the interval to provide a fourth summation. Similarly, the cosine function is squared and summed over the interval to provide a fifth summation. Based on the five values, sinusoids contained in the discrete waveform are detected by subtracting each sinusoid from the discrete waveform to provide an associated residual waveform and detecting each residual waveform whose power is a local minimum as a result of varying the period.

Abstract: An improved method for non-harmonic waveform analysis that permits freedom of selecting intervals and/or frequencies (or periods) for analysis is disclosed. An arbitrary interval of a discrete waveform is multiplied by a sine function having an arbitrary period and the product is summed over the interval to derive a first summation. Similarly, the waveform is multiplied by a cosine function having the same period and the product is summed over the interval to provide a second summation. The sine and cosine functions are multiplied together and the product is summed over the interval to provide a third summation. The sine function is squared and summed over the interval to provide a fourth summation. Similarly, the cosine function is squared and summed over the interval to provide a fifth summation.

Abstract: A novel method of non-harmonic analysis of a physical waveform is disclosed. A digitized wave data is multiplied by a first sine and a first cosine function having a first predetermined period, respectively, and the resulting products are respectively summed over a predetermined interval equal to an integer multiple of the first predetermined period. The resulting summation values are used to determine the amplitudes of the first sine and first cosine functions. A sine and a cosine waveform having the thus determined amplitudes and the first predetermined period are subtracted from the wave data to derive a residual wave data. The above steps are performed on the wave data successively using a second to n-th sine and cosine functions having a second to n-th predetermined periods to derive (n-1) residual wave data. The power of each residual wave data is checked to determine as a first non-harmonic frequency component the sine and cosine waveforms providing a minimum power.

Abstract: The linearity of a circuit is measured by applying a test signal waveform to the circuit under test and then determining the level of the DC component or a certain low frequency component of the waveform as altered by the circuit under test. The test signal waveform has a first value for a first predetermined time period, a second value for a second predetermined time period and a third value for a third predetermined time period, the first and third values being equal in magnitude and polarity to each other, the second value being different in magnitude and polarity from the first and third values. The area of the part of the waveform above zero axis is equal to the area below the zero axis. Once the altered waveform varies in shape from the original waveform, the area of the portions of the altered waveform above and below the zero axis will be different in accordance with the nonlinearity.

Abstract: Disruptive discontinuities resulting from sampling in a time compression and expansion frequency transformation system are minimized by use of comb filters in the form of transversal filters.

Abstract: Disclosed herein is a novel frequency division multiplex system for use in connection with transient signals such as speech and music signals. One embodiment includes a pair of comb filters, the response characteristics of which are staggered so that the pass bands of one comb filter are in alignment with the attenuation bands of the other comb filter. Each channel signal is filtered by its associated comb filter and then combined to develop a comb frequency division duplex (CFDD) signal for transmission over a transmission medium. At the receiving terminal the CFDD signal is decombined into the individual channels and passed through another pair of comb filters, the response characteristic of each comb filter being the same as that of the comb filter in a corresponding input channel. In another embodiment, a recording and playback system is provided to record the CFDD signal, i.e., two channels of information in a single track on disc or tape and to playback such recorded information.