Apparatus and method for reducing multiplicative gain variation distortions in data recording and transmission channels

In combination for use with a data source for providing a sequence of data items

• accumulator means responsive to said sequence of data items for algebraically accumulating said data items in modulo in accordance with a preconditioning function thereby forming a sequence of output partial sums respectively,
• exponentiating means coupled to the output of said accumulator means and responsive to said sequence of output partial sums for sequentially providing an essentially exponential function thereof by sequentially raising a base to a power proportional to said output partial sums respectively, thereby providing a sequence of first signals respectively,
• said first signals being subject to multiplicative distortions which are filterable with respect to said data items thereby providing a sequence of distorted first signals,
• logarithmic converter means responsive to said sequence of distorted first signals for sequentially providing a logarithmic function thereof, respectively, inverse to said exponential function, thereby providing a sequence of second signals respectively,
• said logarithmic converter means converting said multiplicative distortions to additive distortions,
• subtractor means coupled to said logarithmic converter means for providing algebraic differences in modulo between said second signals in accordance with a function inverse to said preconditioning function thereby providing a subtractive operation providing a sequence of third signals representative of said sequence of data items, respectively, with said additive distortions substantially filtered therefrom by said subtractive operation, and
• memory means in said subtractor means for storing at least one of said second signals occurring prior to the currently occurring of said second signals thereby providing signals for said subtractor means to provide said algebraic differences.

In combination for use with a data source of providing a sequence of data items

• exponentiating means responsive to said sequence of data items for sequentially providing an essentially exponential function thereof by sequentially raising a base to a power proportional to said data items respectively,
• cumulative multiplying means coupled to the output of said exponentiating means for providing the cumulative product of said exponential function of said sequence of data items in accordance with a conditioning function, thereby forming a sequence of first signals respectively,
• said first signals being subject to multiplicative distortions which are filterable with respect to said data items thereby providing a sequence of distorted first signals,
• ratio converter means responsive to said sequence of distorted first signals for providing ratios therebetween in accordance with a function inverse to said conditioning function, thereby performing a ratio operation providing a sequence of second signals, respectively, with said multiplicative distortions substantially filtered therefrom by said ratio operation,
• memory means in said ratio converter means for storing at least one of said distorted first signals occurring prior to the currently occurring of said distorted first signals thereby providing signals for said ratio converter means to provide said ratios, and
• logarithmic converter means coupled to the output of said ratio converter means and responsive to said sequence of second signals for sequentially providing a logarithmic function thereof, respectively, inverse to said exponential function, thereby providing a sequence of third signals representative of said sequence of data items respectively.

In combination for use with a data source for providing a sequence of data items

• exponentiating means responsive to said sequence of data items for sequentially providing an essentially exponential function thereof by sequentially raising a base to a power proportional to said data items respectively,
• cumulative multiplying means coupled to the output of said exponentiating means for providing the cumulative product of said exponential function of said sequence of data items in modulo with respect to the exponent in accordance with a conditioning function, thereby forming a sequence of first signals respectively,
• said first signals being subject to multiplicative distortions which are filterable with respect to said data items thereby providing a sequence of distorted first signals,
• ratio converter means responsive to said sequence of distorted first signals for providing ratios therebetween in modulo with respect to the exponent in accordance with a function inverse to said conditioning function, thereby performing a ratio operation providing a sequence of second signals, respectively, with said multiplicative distortions substantially filtered therfrom by said ratio operation,
• memory means in said ratio converter means for storing at least one of said distorted first signals occurring prior to the currently occurring of said distorted first signals thereby providing signals for said ratio converter means to provide said ratios, and
• logarithmic converter means coupled to the output of said ratio converter means and responsive to said sequence of second signals for sequentially providing a logarithmic function thereof, respectively, inverse to said exponential function, thereby providing a sequence of third signals representative of said sequence of data items respectively.

In combination for use with a data source for providing a sequence of data items

• accumulator means responsive to said sequence of data items for algebraically accumulating said data items in accordance with a preconditioning function thereby forming a sequence of output partial sums respectively,
• exponentiating means coupled to the output of said accumulator means and responsive to said sequence of output partial sums for sequentially providing an essentially exponential function thereof by sequentially raising a base to a power proportional to said output partial sums respectively, thereby providing a sequence of first signals respectively,
• said first signals being subject to multiplicative distortions which are filterable with respect to said data items thereby performing a sequence of distorted first signals,
• ratio converter means responsive to said sequence of distorted first signals for providing ratios therebetween, thereby performing a ratio operation providing a sequence of second signals, respectively, with said multiplicative distortions substantially filtered therefrom by said ratio operation,
• memory means in said ratio converter means for storing at least one of said distorted first signals occurring prior to the currently occurring of said distorted first signals thereby providing signals for said ratio converter means to provide said ratios, and
• logarithmic converter means coupled to the output of said ratio converter means and responsive to said sequence of second signals for sequentially providing a logarithmic function thereof, respectively, inverse to said exponential function, thereby providing a sequence of third signals representative of said sequence of data items respectively.

In combination for use with a data source for providing a sequence of data items

• exponentiating means responsive to said sequence of data items for sequentially providing an essentially exponential function thereof by sequentially raising a base to a power proportional to said data items respectively,
• cumulative multiplying means coupled to the output of said exponentiating means for providing the cumulative product of said exponential function of said sequence of data items in accordance with a conditioning function, thereby forming a sequence of first signals respectively,
• said first signals being subject to multiplicative distortions which are filterable with respect to said data items thereby providing a sequence of distorted first signals,
• logarithmic converter means responsive to said sequence of distorted first signals for sequentially providing a logarithmic function thereof, respectively, inverse to said exponential function, thereby providing a sequence of second signals respectively,
• said logarithmic converter means converting said multiplicative distortions to additive distortions,
• subtractor means coupled to said logarithmic converter means for providing algebraic differences between said second signals, thereby performing a subtractive operation providing a sequence of third signals representative of said sequence of data items, respectively, with said additive distortions substantially filtered therefrom by said subtractive operation, and
• memory means in said subtractor means for storing at least one of said second signals occurring prior to the currently occurring of said second signals thereby providing signals for said subtractor means to provide said algebraic differences.

In combination for use with a data source for providing variable data

• preconditioning means responsive to said variable data for preconditioning said data in accordance with a preconditioning function,
• exponentiating means coupled to the output of said preconditioning means and responsive to said preconditioned data for providing an essentially exponential function thereof by raising a base to a power proportional to said preconditioned data thereby providing first signals,
• said first signals being subject to multiplicative distortions which are filterable with respect to said data thereby providing distorted first signals,
• logarithmic converter means responsive to said distorted first signals for providing a logarithmic function thereof, inverse to said exponential function, thereby converting said multiplicative distortions to additive distortions,
• data restoration means coupled to said logarithmic converter means for restoring said logarithmic function of said distorted first signals in accordance with a function inverse to said preconditioning function, thereby providing second signals representative of said variable data with said additive distortions substantially filtered therefrom,
• a source of carrier signal for providing a carrier signal withi information content unrelated to that of said variable data, and
• means for amplitude modulating said carrier signal with said exponential function thereby providing said first signals.

In a digital recording channel having a recording medium, means for writing data items on said medium and means for reading said data items from said medium, each said data item being representable by a selected one of a plurality of amplitudes, the combination comprising

• accumulator means responsive to a sequence of said data items for algebraically accumulating said data items in accordance with a preconditioning function thereby forming a sequence of output partial sums respectively,
• exponentiating means coupled to the output of said accumulator means and responsive to said sequence of output partial sums for sequentially providing an essentially exponential function thereof to said writing means for recording on said medium by sequentially raising a base to a power proportional to said output partial sums respectively,
• said reading means providing a sequence of first signals representative of said recorded exponential function of said output partial sums, respectively, said first signals being subject to multiplicative gain variation distortions of said channel, thereby providing a sequence of distorted first signals,
• logarithmic converter means responsive to said sequence of distorted first signals for sequentially providing a logarithmic function, thereof, respectively, inverse to said exponential function, thereby providing a sequence of second signals respectively,
• said logarithmic converter means converting said multiplicative distortions to additive distortions,
• subtractor means coupled to said logarithmic converter means for providing algebraic differences between said second signals in accordance with a function inverse to said preconditioning function, thereby performing a subtractive operation providing a sequence of third signals representative of said sequence of data items, respectively, with said additive distortions substantially filtered therefrom by said subtractive operation, and
• memory means in said subtractor means for storing at least one of said second signals occurring prior to the currently occurring to said second signals thereby providing signals for said subtractor means to provide said algebraic differences.

In a digital recording channel having a recording medium, means for writing data items on said medium and means for reading said data items from said medium, each said data item being represented by a selected one of a plurality of amplitudes, the combination comprising

• accumulator means responsive to a sequence of said data items for algebraically accumulating said data items in modulo in accordance with a preconditioning function thereby a sequence asequence of output partial sums respectively,
• exponentiating means coupled to the output of said accumulator means and responsive to said sequence of output partial sums for sequentially providing an essentially exponential function thereof to said writing means for recording on said medium by sequentially raising a base to a power proportional to said output partial sums respectively,
• said reading means providing a sequence of first signals representative of said recorded exponential function of said output partial sums, respectively, said first signals being subject to multiplicative gain variation distortions of said channel thereby providing a sequence of distorted first signals,
• logarithmic converter means responsive to said sequence of distorted first signals for sequentially providing a logarithmic function thereof, respectively, inverse to said exponential function, thereby providing a sequence of second signals respectively,
• said logarithmic converter means converting said multiplicative distortions to additive distortions,
• subtractor means coupled to said logarithmic converter means for providing algebraic differences in modulo between said second signals in accordance with a function inverse to said preconditioning function, thereby performing a subtractive operation providing a sequence of third signals representative of said sequence of data items, respectively, with said additive distortions substantially filtered therefrom by said subtractive operation, and
• memory means in said subtractor means for storing at least one of said second signals occurring prior to the currently occurring of said second signals thereby providing signals for said subtractor means to provide said algebraic differences.

A method for reducing multiplicative distortions in a data channel for conveying a sequence of data items comprising the steps of

• algebraically accumulating said data items in accordance with a preconditioning function thereby forming a sequence of output partial sums respectively,
• exponentiating said sequence of output partial sums by sequentially providing an essentially exponential function thereof by sequentially raising a base to a power proportional to said output partial sums respectiely, thereby providing a sequence of first signals respectively,
• conveying said sequence of first signals on said channel whose characteristics impart multiplicative distortions thereto thereby providing a sequence of distorted first signals,
• logarithmically converting said sequence of distorted first signals by providing a logarithmic function thereof, respectively, inverse to said exponential function, thereby providing a sequence of second signals respectively,
• said logarithmically converting step converting said multiplicative distortions to additive distortions,
• algebraically subtracting said second signals from each other to provide algebraic differences therebetween in accordance with a function inverse to said preconditioning function thereby providing a sequence of third signals representative of said sequence of data items, respectively, with said additive distortions substantially filtered therefrom by said subtracting step, and
• storing at least one of said second signals occurring prior to the currently occurring of said second signals thereby providing the signals for said subtracting step.