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41 | However, RF DACs and DDS control systems do have limitations. Depending on the chosen code words, a phase truncation can occur and introduce errors and even spurs. Reference clock jitter, along with RF DAC quantization and linearity errors, can introduce both noise and harmonics. Some of these added spurs, harmonics, and noise can be mitigated. To help reduce undesirable signal degradation with DDS systems, engineers can select a low-phase- noise oscillator for the reference, appropriately compensate for environmental factors of jitter, use frequency division to reduce reference oscillator jitter further, use the highest possible sampling frequency to allow for oversampling, and otherwise optimize the design to minimize interference and noise in the signal path. Digital Frequency Translation & Filtering Digital frequency translation functions are commonly used in DSP transmitter, receiver, and transceiver applications. This approach competes with using RF mixers, doublers, and other frequency-translation hardware to upconvert or downconvert signals. However, many RF applications operate at a spectrum beyond the capability of accessible RF DACs and RF ADCs, and an analog frequency-translation stage may be necessary to convert the signal to an IF within the capability of the digital hardware. With digital frequency translation, a swath of signal bandwidth is digitized by an RF ADC and may be filtered and otherwise digitally processed to remove noise and unwanted signal content before digital downconversion to a baseband frequency for further processing and demodulation. In the case of transmission, developers can use DSP techniques to fully generate the baseband signal with modulation at extremely high fidelity, then perform digital upconversion before being synthesized using an RF DAC. Digital frequency translation has additional nuances, such as the need to filter the unwanted image and sidebands created by the RF ADC and DDS during digital downconversion. Developers can use downsampling to help remove the unwanted frequency components created by digital downconversion outside the desired signal bandwidth. Interpolation filtering is helpful during digital upconversion, which can be achieved with a single interpolation filter but is often performed with multiple simpler interpolation filters when implemented with digital hardware such as an FPGA. A wide variety of strategies exist to implement digital filters, which can be highly effective at mitigating spurs, noise, and harmonics. Higher-complexity digital filters provide enhanced filtering performance, but at the cost of greater hardware complexity. Therefore, it is often much more efficient to use a cascade of several simpler filter stages rather than a single complex filter stage to meet the performance goal. For example, finite impulse response (FIR) filters and infinite impulse response (IIR) filters are often used in digital RF filtering applications. FIR filters can exhibit precise linear phases and ensure stability. They generally require linear design methods, are hardware efficient, and the filter startup transients have a finite duration. Compared with IIR filters, FIR filters typically need to be more complex to reach the same performance level but introduce a much greater delay. Beamforming, Beamsteering, and MIMO Beamforming uses multiple antenna elements in an array with coordinated phase and amplitude responses to direct the antenna pattern in a desired direction. This method uses constructive and destructive interference to form a desired antenna pattern, with lobes and nulls generated via the antenna element phase and amplitude control. Beamsteering is an advancement of beamforming where the antenna pattern is dynamically changed using the phase of the signals in real time, and not the signal path elements as with beamforming. Both techniques are used with modern, advanced communication systems, such as 5G and Wi-Fi 7. MIMO is the use of multiple transmitter (TX) and receiver (RX) antennas to create spatial multiplexing among the various paths between the TX and RX antenna elements. Using signals within the same bandwidth that travel over different paths from TX to RX can result in redundant data transmission. The signals can carry different information to effectively multiply the throughput. The RX in a MIMO system takes

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