Hi Sazia,
See the other thread for a suggested workflow. It looks like you already have a core microbiome calculated in QIIME. As long as the original OTU table contained only reference ids (e.g. came from closed reference OTU picking), you should be able to use your core_table_75.biom as the input to normalize_by_copy_number.py and/or predict_traits.py in PICRUSt.
The effect of running this table through copy number normalization and metagenome prediction in PICRUSt would be to ask "What is the predicted gene content of my samples, considering only the pool of microbes present in 75% of samples?". If that is the type of microbiome functional analysis you are after, then you should be set.
Alternatively, you might be interested in asking about what functions are core to the whole microbiome (vs. the functions of the core microbes). In that case, you could run PICRUSt on your whole OTU table (before doing a core microbiome analysis). Then you could select only core functions based on prevalence across 75% of samples. You may be able to do this with compute_core_microbiome.py, although I haven't tried it with functional data. If you do use that script, you'll likely need to change the --otu_md option, which specifies the metadata key for describing the output. It defaults to taxonomy, which isn't present in PICRUSt metagenome predictions.
Best,
Jesse