Fine resolution selection of the sample rate is not available in digital storage oscilloscopes (DSOs), so the user has to rely on offline processing to cope with such need. The paper first discusses digital signal processing based methods that allow changing the sampling rate by means of digital resampling approaches. Then, it proposes a digital circuit that, if included in the acquisition channel of a digital storage oscilloscope, between the internal analog-to-digital converter (ADC) and the acquisition memory, allows the user to select any sampling rate lower than the maximum one with fine resolution. The circuit relies both on the use of a short digital filter with dynamically generated coefficients and on a suitable memory management strategy. The output samples produced by the digital circuit are characterized by a sampling rate that can be incoherent with the clock frequency regulating the memory access. Both a field programmable gate array (FPGA) implementation and an application specific integrated circuit (ASIC) design of the proposed circuit are evaluated.

Digital Storage Oscilloscopes (DSOs) conjugate high performance with large number of features and flexibility. The basic structure, based on fast Analog to Digital Converter (ADC) and memory, is augmented with several components for channel matching and bandwidth improvement, and processors that provide visualization, frequency processing, jitter and stability measurement, etc. Unfortunately, fine resolution in sample rate selection is not available, such that for several applications the user must run complex measurement procedures that require data download and offline processing. The paper proposes a dedicated digital circuit that offers fine control of the time-base by real time downsampling the input stream at an almost arbitrary sampling rate. The proposed circuit implements a series of operations involving real-time data filtering, defragmentation and packing, which are not considered by alternative approaches, like those based on polyphase filters, that offer very limited choices for the sampling rate. The circuit is designed to work in conjunction with the highest performance DSOs that use a multichannel architecture. Design rules for circuit design are provided together with implementation results in 14nm FinFET technology. When designed for an architecture with 64 channels with 8bit input samples the circuit works in real time with a sampling rate of 220 GSps running at 3.42 GHz, with a silicon footprint of 0.17 mm 2 and a power dissipation of 0.85W.

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The time-base used by digital storage oscilloscopes allows limited selections of the sample rate, namely constrained to a few integer submultiples of the maximum sample rate. This limitation offers the advantage of simplifying the data transfer from the analog-to-digital converter to the acquisition memory, and of assuring stability performances, expressed in terms of absolute jitter, that are independent of the chosen sample rate. On the counterpart, it prevents an optimal usage of the memory resources of the oscilloscope and compels to post processing operations in several applications. A time-base that allows selecting the sample rate with very fine frequency resolution, in particular as a rational submultiple of the maximum rate, is proposed. The proposal addresses the oscilloscopes with time-interleaved converters, that require a dedicated and multifaceted approach with respect to architectures where a single monolithic converter is in charge of signal digitization. The proposed time-base allows selecting with fine frequency resolution sample rate values up to 200 GHz and beyond, still assuring jitter performances independent of the sample rate selection.

Approximate computing, frequently used in error tolerant applications, aims to achieve higher circuit performances by allowing the possibility of inaccurate results, rather than guaranteeing a correct outcome. Many contributions target the binary multiplier aiming to minimize the complexity of this common yet power-hungry circuit. Approximate recursive multipliers are low-power designs that exploit approximate building blocks to scale up to their final size. In this paper, we present two novel 4x4 approximate multipliers obtained by carry manipulation. They are used to compose 8x8 designs with different error-precision trade-off. The final circuits exhibit a competitive behavior in terms of error while reducing the power dissipation when compared to state-of-the-art proposals. The proposed multipliers and state-of-the-art designs found in the literature, have been synthesized targeting a 14nm FinFET technology to determine the electrical characteristics. Compared with an exact 8×8 multiplier, the least dissipative design proposed in this paper reduces power consumption and silicon area by 46%, and minimum delay by 21%. It also consumes 14% less power than the least power-hungry recursive circuit found in the literature, while offering 81% higher accuracy. Ιmage processing applications and a convolutional neural network are shown to demonstrate the effectiveness of the proposed multipliers.