Low-frequency pulse-jitter measurement with the uGMRT I : PSR J0437$-$4715

High-precision pulsar timing observations are limited in their accuracy by the jitter noise that appears in the arrival time of pulses. Therefore, it is important to systematically characterise the amplitude of the jitter noise and its variation with frequency. In this paper, we provide jitter measurements from low-frequency wideband observations of PSR J0437$-$4715 using data obtained as part of the Indian Pulsar Timing Array experiment. We were able to detect jitter in both the 300 - 500 MHz and 1260 - 1460 MHz observations of the upgraded Giant Metrewave Radio Telescope (uGMRT). The former is the first jitter measurement for this pulsar below 700 MHz, and the latter is in good agreement with results from previous studies. In addition, at 300 - 500 MHz, we investigated the frequency dependence of the jitter by calculating the jitter for each sub-banded arrival time of pulses. We found that the jitter amplitude increases with frequency. This trend is opposite as compared to previous studies, indicating that there is a turnover at intermediate frequencies. It will be possible to investigate this in more detail with uGMRT observations at 550 - 750 MHz and future high sensitive wideband observations from next generation telescopes, such as the Square Kilometre Array. We also explored the effect of jitter on the high precision dispersion measure (DM) measurements derived from short duration observations. We find that even though the DM precision will be better at lower frequencies due to the smaller amplitude of jitter noise, it will limit the DM precision for high signal-to-noise observations, which are of short durations. This limitation can be overcome by integrating for a long enough duration optimised for a given pulsar.